NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

 

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions: An algebraic expression contains variables, numbers, and operations. In this article, you will get NCERT solutions for class 7 maths chapter 12 algebraic expressions. There are three types of algebraic expressions

  • Monomial:-An algebraic expression with only one term is known as a monomial. Example: 2x, 3xy, 4xyz, etc. 
  • Binomial:- An algebraic expression with two, unlike terms, is known as binomial. Example: 2x+3xy
  • Trinomial and Polynomials:- An algebraic expression with more than one unlike term is known as a polynomial. Example: 2x+3xy+4xyz+abc. Binomial and trinomial are also polynomial.

The terms containing the same algebraic factors (i.e those which contain variables) are like terms, for example, 3xy and 5xy are like terms since both have the algebraic factors (i.e those which contain variables) x and y. The term which contains different algebraic factors is unlike terms. For example, 2x and 3xy are unlike terms. In solutions of NCERT for class 7 maths chapter 12 algebraic expressions, you will get questions related to solving all three types of algebraic expressions. Also, you will learn the addition and subtraction of algebraic expression. If an algebraic expression contains the sum of more than one like terms they can be combined to form a single term. For example, 14x+6x+20y+10x can be added and can be written as 30x+20y. There are many problems in the CBSE NCERT solutions for class 7 maths chapter 12 algebraic expressions which will give more clarity of the concepts. Check NCERT solutions from class 6 to 12 fro science and maths by clicking on the above link.

The main topics of the NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions are: 

12.1 Introduction

12.2 How Are Expressions Formed?

12.3 Terms Of An Expression

12.4 Like And Unlike Terms

12.5 Monomials, Binomials, Trinomials And Polynomials

12.6 Addition And Subtraction Of Algebraic Expressions

12.7 Finding The Value Of An Expression

12.8 Using Algebraic Expressions – Formulas And Rules

This chapter is important for our coming classes. We must practice questions of this chapter and must be able to solve problems very fastly.

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions are given below:

Solutions of NCERT for class 7 maths chapter 12 algebraic expressions topic 12.2 how are expressions formed?

Question: Describe how the following expressions are obtained:

         7xy+5, x^{2} y,4x^{2}-5x

Answer:

7xy+5

the above expression is obtained by adding 7xy with 5. Here 7xy is obtained by multiplying 7,x and y

4 x^2-5x

the above expression is obtained by subtracting the product of 5 and x from the product of 4,x and x

CBSE NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.3 terms of an expression

Question:1 What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression:

              8y+3x^{2},7mn-4,2x^{2}y.

Answer:

 8y+3x^{2} The terms in the expression are 

8y\ and\ 3x^{2}    

8y+3x^{2} is obtained by adding the product of 8 and y with the product of 3 x and x

the tree diagram for the expression is given below

7mn-4 has two terms 7mn and 4 and the expression is obtained by subtracting 4 from the product of 7,m and n. The tree diagram is shown below.

2x^2y has only one term, that is the expression itself.

The expression is formed by multiplying 4 terms 2, x, x and y. The tree diagrams are shown below

 

Question:2 Write three expressions each having 4 terms.

Answer:

We can write as many expressions we need with 4 terms. Following are a few examples of expression with 4 terms

\\ a+b+c+d\\ab+bc+cd+ad\\abc+bcd+acd+abcd

Question: Identify the coefficients of the terms of following expressions:

             4x-3y,a+b+5,2y+5,2xy

Answer:

i) 4x-3y has two terms 4x and -3y

the coefficient of x is 4 and the coefficient of y is -3

ii) a+b+5 has 3 terms a,b and a constant that is 5.

the coefficient of a is 1 and b is also 1. Constant terms have no coefficient 

iii) 2y+5 has two terms 2y and 5 which is constant.

 The coefficient of y is 2. Constant terms have no coefficient 

iv) 2xy has only one term which is 2xy and the coefficient of xy is 2

NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.4 like and unlike terms

Question:1(i)  Group the like terms together from the following:

  12x,  12 ,  -25x,  -25-25y1x12yy

Answer:

The like terms are grouped below

Group 1: 12x-25xx

Group 2: -25y12yy

Group 3: 12-251

Solutions of NCERT for class 7 maths chapter 12 algebraic expressions topic 12.5 monomials, binomials, trinomials and polynomials

Question: Classify the following expressions as a monomial, a binomial or a trinomial:

           a,a+b.ab+a+b,ab+a+b-5,xy,xy+5,5x^{2}-x+2,4pq-3q+5p,7,4m-7n+10,4mn+7.

Answer:

Monomial: a, xy, 7

binomial: a+b, xy+5, 4mn+7

Trinomial: ab+a+b, 5x2-x+2, 4pq-3q+5p, 4m-7n+10

Polynomial with 4 terms: ab+a+b-5

Solutions of NCERT for class 7 maths chapter 12 algebraic expression-Exercise: 12.1

Question:1(i)  Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Subtraction of z from y.

Answer:

Subtraction of z from y: y-z

Question:1(ii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation.

 One-half of the sum of numbers x and y.

Answer:

Sum of numbers x and y = x + y

One half of the sum of numbers x and y

=\frac{x+y}{2}

Question:1(iv) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

One-fourth of the product of numbers p and q.

Answer:

Product of the numbers p and q = p \times q=pq

One-fourth of the product of numbers p and q

=\frac{pq}{4}

Question:1(v) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

 Numbers x and y both squared and added.

Answer:

Number x squared =x^{2}

Number y squared = y^{2}

Numbers x and y both squared and added = x^{2}+ y^{2}

Question:1(vi) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation. 

 Number 5 added to three times the product of numbers m and n.

Answer:

Product of numbers m and n =m\times n=mn

Number 5 added to three times the product of numbers m and n = =3\times mn+5=3mn+5

Question:1(vii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Product of numbers y and z subtracted from 10.

Answer:

Product of numbers y and z =y\times z=yz

Product of numbers y and z subtracted from 10 =10-yz

Question:1(viii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Sum of numbers a and b subtracted from their product.

Answer:

Sum of numbers a and b = a + b

Product of the numbers a and b =a\times b=ab

Sum of numbers a and b subtracted from their product = ab - (a+b) = ab - a - b.

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams. (a) x-3

Answer:

Expression : x - 3

Terms in the above expression: x and -3

Tree diagram for the given expression 

 

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (b)   1+x+x^{2}

Answer:

Expression: 1 + x + x^2

Tems in the above expression: 1, x \and\ x^2

Factors of x2: x and x

Tree diagram for the given expression 

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (c)  y-y^{3}

Answer:

Expression: y - y3

Tems in the above expression: y and -y3

Factors of -y3: -1, y, y and y

Tree diagram for the given expression 

Question:2(i) Identify the terms and their factors in the following expressions

 Show the terms and factors by tree diagrams. (d)  5xy^{2}+7x^{2}y

Answer:

Expression: 5xy2 + 7x2y

Terms in the above expression: 5xy2 and 7x2y

Factors of  5xy2: 5, x, y and y

Factors of 7x2y: 7, x, x and y

Tree diagram for the given expression 

Question:2(i) Identify the terms and their factors in the following expressions 

Show the terms and factors by tree diagrams (e)  -ab+2ab^{2}-3a^{2}

Answer:

Expression: -ab + 2ab2 - 3a2

Terms in the above expression: -ab, 2ab2 and -3a2

Factors of -ab: -1, a and b

Factors of 2ab2: 2, a, b and b

Factors of -3a2: -1, 3, a and a

Tree diagram for the given expression 

Question:2(ii) Identify terms and factors in the expressions given below:

    (a)  -4x+5

Answer:

Expression: -4x + 5

Terms in the above expression: -4x and 5

Factors of -4x: -1, 4 and x

Factors of 5: 5

Question:2(ii) Identify terms and factors in the expressions given below:

           (b)  -4x+5y

Answer:

Expression: -4x + 5y

Terms in the above expression: -4x and 5y

Factors of  -4x: -1, 4 and x

Factors of 5y: 5 and y

Question:2(ii) Identify terms and factors in the expressions given below:

         (c)  5y+3y^{2}

Answer:

Expression: 5y + 3y2

Terms in the above expression: 5y and 3y2

Factors of  5y: 5 and y

Factors of 3y2: 3, y and y

Question:2(ii) Identify terms and factors in the expressions given below:

           (d)  xy+2x^{2}y^{2}

Answer:

Expression: xy + 2x2y2

Terms in the above expression: xy and 2x2y2

Factors of  xy: x and y

Factors of 2x2y2: 2, x, x, y and y

Question:2(ii) Identify terms and factors in the expressions given below:

                (e)  pq+q

Answer:

Expression: pq + q

Tems in the above expression: pq and q

Factors of  pq: p and q

Factors of q: q

Question:2(ii) Identify terms and factors in the expressions given below: 

         (f)  1.2 \; ab-2.4\; b+3.6\; a

Answer:

Expression: 1.2ab - 2.4b + 3.6a

Tems in the above expression: 1.2ab, -2.4b and 3.6a

Factors of  1.2ab: 1.2, a and b

Factors of -2.4b: -1, 2.4 and b

Factors of 3.6a: 3.6 and a

Question:2(ii) Identify terms and factors in the expressions given below: 

            (g)  \frac{3}{4}x+\frac{1}{4}

Answer:

Expression: \frac{3}{4}x+\frac{1}{4}

Terms in the above expression: \frac{3}{4}x and \frac{1}{4}

Factors of  \frac{3}{4}x:    \frac{3}{4} and x

Factors of  \frac{1}{4}:   \frac{1}{4}

Question:2(ii) Identify terms and factors in the expressions given below:

                 (h)  0.1\; p^{2}+0.2\; q^{2}

Answer:

Expression: 0.1p2 + 0.2q2

Tems in the above expression:0.1p2 and 0.2q2

Factors of  0.1p2: 0.1, p and p

Factors of  0.2q2: 0.2, q and q 

Question:3(i) Identify the numerical coefficients of terms (other than constants) in the following expressions:

  5-3t^{2}

Answer:

Expression: 5 - 3t2

Tems in the above expression: 5 and -3t2

Coefficient of -3t2: -3

Question:3(ii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

 1+t+t^{2}+t^{3}

Answer:

Expression: 1 + t + t2 + t3

Terms in the above expression: 1, t, t2 and t3

Coefficient of t is 1

Coefficient of t is 1

Coefficient of t3: is 1

Question:3(iii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

  x+2xy+3y

Answer:

Expression: x + 2xy + 3y

Terms in the above expression: x, 2xy and 3y

Coefficient of x: 1

Coefficient of 2xy: 2

Coefficient of 3y: 3

Question:3(iv) Identify the numerical coefficients of terms (other than constants) in the following expressions:

 100m+1000n

Answer:

Expression: 100m + 1000n

Terms in the above expression: 100m and 1000n

Coefficient of 100m: 100

Coefficient of 1000n: 1000

Question:3(v) Identify the numerical coefficients of terms (other than constants) in the following expressions:

  -p^{2}q^{2}+7pq

Answer:

Expression: -p2q2 + 7pq

Tems in the above expression: -p2q2 and 7pq

Coefficient of -p2q2: -1

Coefficient of 7pq: 7

Question:3(vi) Identify the numerical coefficients of terms (other than constants) in the following expressions:

  1.2\; a+0.8\; b

Answer:

Expression: 1.2a + 0.8b

Terms in the above expression: 1.2a and 0.8b

Coefficient of 1.2a: 1.2

Coefficient of 0.8b: 0.8

Question:3(vii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

  3.14\; r^{2}

Answer:

Expression: 3.14r2

Terms in the above expression: 3.14r2

Coefficient of 3.14ris 3.1

Question:3(viii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

  2(l+b)

Answer:

Expression: 2(l + b) = 2l + 2b

Tems in the above expression: 2l and 2b

Coefficient of 2l: 2

Coefficient of 2b: 2

Question:3(ix) Identify the numerical coefficients of terms (other than constants) in the following expressions:

 0.1\; y+0.01\; y^{2}

Answer:

Expression: 0.1y + 0.01y2

Tems in the above expression: 0.1y and 0.01y2

Coefficient of 0.1y is 0.1

Coefficient of 0.01y is 0.01

Question:4(a) Identify terms which contain x and give the coefficient of x.

             (i)  y^{2}x+y

Answer:

Expression: y2x + y

Terms with x: y2x

Coefficient of x in y2x: y2

Question:4(a) Identify terms which contain x and give the coefficient of x.

      (ii)  13y^{2}-8yx

Answer:

Expression: 13y2 - 8yx

Terms with x: -8yx

Coefficient of x in -8yx: -8y

Question:4(a) Identify terms which contain x and give the coefficient of x.    

   (iii) x+y+2

Answer:

Expression: x + y + 2

Terms with x: x

Coefficient of x in x: 1

Question:4(a) Identify terms which contain x and give the coefficient of x.

    (iv)  5+z+zx

Answer:

Expression: 5 + z + zx

Terms with x: zx

Coefficient of x in zx: z

Question:4(a) Identify terms which contain x and give the coefficient of x .

(v)  1+x+xy

Answer:

Expression: 1 + x + xy

Terms with x: x and xy

Coefficient of x in x: 1

Coefficient of x in xy: y

Question:4(a) Identify terms which contain x and give the coefficient of x.

              (vi)  12xy^{2}+25

Answer:

Expression: 12xy2 + 5

Terms with x: 12xy2 

Coefficient of x in 12xy2: 12y2

Question:4(a) Identify terms which contain x and give the coefficient of x. 

             (vii)  7x+xy^{2}

Answer:

Expression: 7x + xy2

Terms with x: 7x and xy2

Coefficient of x in 7x: 7

Coefficient of x in xy2: y2

Question:4(b) Identify terms which contain y^{2} and give the coefficient of  y^{2}.

(i)  8-xy^{2}

Answer:

Expression: 8 - xy2

Terms with y2: -xy2

Coefficient of y2 in -xy2: -x

Question:4(b) Identify terms which contain y^{2} and give the coefficient of y^{2} .

(ii)  5y^{2}+7x

Answer:

Expression: 5y2 + 7x

Terms with y2: 5y2

Coefficient of y2 in 5y2: 5

Question:4(b) Identify terms which contain y^{2} and give the coefficient of y^{2} .

             (iii)  2x^{2}y-15xy^{2}+7y^{2}

Answer:

Expression: 2x2y -15xy2 + 7y2

Terms with y2: -15xy2 and 7y2

Coefficient of y2 in -15xy2: -15x

Coefficient of y2 in 7y2: 7

Question:6(i) State whether a given pair of terms is of like or unlike terms.

  1,100

Answer:

  (i)  1,100 are Like terms.

Question:6(ii) State whether a given pair of terms is of like or unlike terms.

-7x,\frac{5}{2}x

Answer:

  (ii)  -7x,\frac{5}{2}x   are Like terms

Question:6(iii) State whether a given pair of terms is of like or unlike terms.

  -29x, -29y

Answer:

Unlike since y and x are unlike terms

Question:6(iv) State whether a given pair of terms is of like or unlike terms. 

   14xy,42yx

Answer:

like terms since both the terms contain xy and only the coefficient is different

Question:6(v) State whether a given pair of terms is of like or unlike terms.

  4m^{2}p,4mp^{2}

Answer:

Unlike since m^2p \ and \ mp^2 are different

Question:6(vi) State whether a given pair of terms is of like or unlike terms. 

 12xz,12x^{2}z^{2}

Answer:

Unlike since xz \ and\ x^2z are unlike terms

Question:7(a) Identify like terms in the following:

   -xy^{2},-4yx^{2},8x^{2},2xy^{2},7y,-11x^{2},-100x,-11yx,20x^{2}y,-6x^{2},y,2xy,3x

Answer:

Like terms are

(i) -xyand 2xy

(ii) -4x2y and 20x2y

(iii) 8x2, -11x2 and -6x2

(iv) 7y and y

(v) -100x and 3x

(vi) -11yx and 2xy

Question:7(b) Identify like terms in the following: 

  10pq,7p,8q,-p^{2}q^{2},-7qp,-100q,-23,12q^{2}p^{2},-5p^{2},41,2405p,78qp,13p^{2}q,qp^{2},701p^{2}

Answer:

Like terms are

(i) 10pq, -7qp and 78qp

(ii) 7p and 2405p

(iii) 8q and -100q

(iv) -p2q2 and 12q2p2

(vii) -23 and 41

(viii) -5p2 and 701p2

(ix) 13p2q and qp2

CBSE NCERT solutions for class 7 maths chapter 12 algebraic expressions topic 12.6 subtopic adding and subtracting general algebraic expressions

Question:(i) Add and subtract

  m-n,m+n

Answer:

Adding

 m-n,m+n

Will give the result as follows

m-n+m+n=2m

Subtracting 

m-n,m+n

Will give the result as follows

m-n-(m+n)=m-n-m-n=-2n

Question:(ii) Add and subtract

 mn+5-2,mn+3

Answer:

adding the following terms

mn+5-2,mn+3

we will get

mn+5-2+mn+3=2mn+6

Subtracting 

mn+5-2,mn+3

We will get

mn+5-2-(mn+3)=mn+5-2-mn-3=0

CBSE NCERT solutions for class 7 maths chapter 12 algebraic expression-Exercise: 12.2

Question:1(i) Simplify combining like terms:

  21b-32+7b-20b

Answer:

21b - 32 + 7b -20b

= (21 + 7 - 20)b -32

= 8b - 32

The simplified expression is 8b - 32.

Question:1(ii) Simplify combining like terms:

  -z^{2}+13z^{2}-5z+7z^{3}-15z

Answer:

-z^{2}+13z^{2}-5z+7z^{3}-15z

-z2 + 13z2 - 5z + 7z3 - 15z

= (-1 + 13)z2 + (-5 - 15)z +7z3

=12z2 - 20z + 7z3

The simplified expression is 12z2 - 20z + 7z3

Question:1(iii) Simplify combining like terms:

  p-(p-q)-q-(q-p)

Answer:

p - (p - q) - q - (q - p)

= p - p + q - q - q + p

= p - p + p + q - q -q

= p - q

The simplified expression is p - q.

Question:1(iv) Simplify combining like terms: 

  3a-2b-ab-(a-b+ab)+3ab+b-a

Answer:

3a - 2b - ab - (a - b + ab) + 3ab + b - a

= 3a - 2b - ab - a + b - ab + 3ab + b - a

= (3 - 1 - 1)a + (-2 + 1 +1)b + (-1 - 1 + 3)ab

= a + ab

The simplified expression is a + ab.

Question:1(v) Simplify combining like terms: 

   5x^{2}y-5x^{2}+3yx^{2}-3y^{2}+x^{2}-y^{2}+8xy^{2}-3y^{2}

Answer:

5x2y - 5x2 + 3yx2 - 3y2 + x2 - y2 + 8xy2 - 3y2

= (5 + 3 )x2y + (-5 + 1)x2 + (-3 - 1 - 3)y2 + 8xy2

= 8x2y - 4x2 - 7y2 + 8xy2

The simplified expression is 8x2y - 4x2 - 7y2 + 8xy2

Question:1(vi) Simplify combining like terms:

 (3y^{2}+5y-4)-(8y-y^{2}-4)

Answer:

(3y2 + 5y - 4) - (8y - y2 - 4)

= 3y2 + 5y - 4 - 8y + y2 + 4

= (3 + 1)y2 + (5 - 8)y - 4 + 4

= 4y2 - 3y 

The simplified expression is 4y2 - 3y 

Question:4(a) What should be added to x^{2}+xy+y^{2} to obtain 

2x^{2}+3xy?

Answer:

Let the term be a which must be added to x2 + xy + y2 to obtain 2x2 + 3xy

\\a + x^2 + xy + y^2 = 2x^2 + 3xy \\a = 2x^2 + 3xy - (x^2 + xy + y^2) \\a = (2-1)x^2 + (3 - 1)xy -y^2 \\a = x^2 + 2xy - y^2

x2 + 2xy - yshould be added to x2 + xy + y2 to obtain 2x2 + 3xy

Question:4(b) What should be subtracted from 2a+8b+10  to get 

-3a+7b+16 ?

Answer:

Let the term be c which must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

\\2a + 8b + 10 - c = -3a + 7b + 16 \\c = 2a + 8b + 10 - (-3a + 7b + 16) \\c = 2a + 8b + 10 + 3a - 7b - 16 \\c = (2 + 3)a + (8 - 7)b + 10 - 16 \\c = 5a + b - 6

5a + b - 6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

Question:What should be taken away from 3x^{2}-4y^{2}+5xy+20  to obtain 

-x^{2}-y^{2}+6xy+20 ?

Answer:

Let the term be a which must be taken away from 3x2 - 4y2 + 5xy + 20 to obtain -x2 - y2 + 6xy + 20

\\3x^2 - 4y^2 + 5xy + 20 - a = -x^2 - y^2 + 6xy + 20 \\a = 3x^2 - 4y^2 + 5xy + 20 - ( -x^2 - y^2 + 6xy + 20 ) \\a = 3x^2 - 4y^2 + 5xy + 20 + x^2 + y^2 - 6xy - 20 \\a = ( 3 + 1 )x^2 + ( -4 + 1 )y^2 + ( 5 - 6 )xy + 20 - 20 \\a = 4x^2 - 3y^2 - xy

4x2 - 3y2 - xy must be taken away from 3x2 - 4y2 + 5xy + 20 to obtain -x2 - y2 + 6xy + 20

Question:6(a) From the sum of 3x-y+11 and-y-11, subtract 3x-y-11.

Answer:

\\( 3x - y + 11 + ( - y - 11 ) ) - ( 3x - y - 11 ) \\= 3x - y + 11 - y - 11 - 3x + y + 11 \\= ( 3 - 3 )x + ( -1 - 1 + 1)y + 11 - 11 + 11 \\= -y + 11

On subtracting 3x - y - 11 from the sum of 3x - y + 11 and -y - 11 we get -y + 11

Question:6(b) From the sum of 4+3x and 5-4x+2x^{2},subtract the sum of 3x^{2}-5x and -x^{2}+2x+5.

Answer:

\\( 4 + 3x + ( 5 - 4x + 2x^2) ) - ( 3x^2 - 5x + ( -x^2 + 2x + 5) \\= (4 + 3x + 5 - 4x + 2x^2 ) - ( 3x^2 - 5x -x2 + 2x + 5) \\= 4 + 3x + 5 - 4x + 2x^2 - 3x^2 + 5x + x^2 - 2x - 5 \\=4 + 5 - 5 + ( 3 - 4 + 5 - 2 )x + ( 2 - 3 + 1 )x^2 \\=4 + 2x

On subtracting the sum of 3x^{2}-5x and -x^{2}+2x+5 from the sum of  4+3x and 5-4x+2x^{2} we get 4+2x

NCERT solutions for class 7 maths chapter 12 algebraic expression-Exercise: 12.3

Question:1(i) If m=2, find the value of:

  m-2

Answer:

(i) m - 2

= 2 - 2

 = 0

If m = 2 the value of m - 2 = 0

Question:1(ii) If m=2, find the value of:

 3m-5

Answer:

\\3m - 5 \\= 3 \times 2 - 5 \\= 6 - 5 \\= 1

If m = 2 the value of 3m - 5 = 1

Question:1(iii) If m=2, find the value of:

  9-5m

Answer:

\\9 - 5m \\= 9 - 5 \times 2 \\= 9 - 10 \\= -1

If m = 2 the value of 9 - 5m = -1

Question:1(iv) If  m=2, find the value of:

  3m^{2}-2m-7

Answer:

\\3m^2 - 2m - 7 \\= 3 \times 2^2 - 2 \times 2 - 7 \\= 12 - 4 - 7 \\= 1

If m = 2 the value of 3m2 - 2m - 7 = 1

Question:1(v) If   find the value of:             (v)  If m=2,  find the value of:

  \frac{5m}{2}-4

Answer:

\frac{5m}{2}-4

=\frac{5\times 2}{2}-4

= 5 - 4

= 1

If m = 2 the value of \frac{5m}{2}-4 = 1

Question:2(i) If p=-2, find the value of:

  4p+7

Answer:

\\4p + 7 \\= 4 \times ( -2 ) + 7 \\= -8 + 7 \\= -1

If p = -2 the value of 4p + 7 = -1

Question:2(ii) If p=-2,  find the value of:

 -3p^{2}+4p+7

Answer:

\\-3p^2 + 4p + 7 \\= -3 x ( -2 )^2 + 4 x ( -2 ) + 7 \\= -12 - 8 + 7 \\= -13

If p = -2 the value of -3p2 + 4p + 7 = -13

Question:2(iii) If p=-2,  find the value of:

  -2p^{3}-3p^{2}+4p+7

Answer:

\\-2p3 - 3p2 + 4p + 7 \\= - 2 \times ( -2)^3 - 3 \times ( -2 )^2 + 4 \times ( -2 ) + 7 \\= 16 - 12 - 8 + 7 \\= 3

If p = -2 the value of -2p3 - 3p2 + 4p + 7 = 3

Question:3(i) Find the value of the following expressions, when x=-1:

 2x-7

Answer:

\\2x - 7 \\= 2 \times ( -1 ) - 7 \\= -2 - 7 \\= -9

If x = -1 the value of 2x - 7 = -9

Question:3(ii)Find the value of the following expressions, when  

x=-1:

  -x+2

Answer:

-x + 2

= -( -1 ) + 2

= 1 + 2

= 3

If x = -1 the value of -x + 2 = 3

Question:3(iii) Find the value of the following expressions, when x=-1:

 x^{2}+2x+1

Answer:

\\x^2 + 2x + 1 \\= ( -1 )^2 + 2 \times ( -1 ) + 1 \\= 1 - 2 + 2 \\= 0

If x = -1 the value of x2 + 2x + 1 = 0

Question:3(iv) Find the value of the following expressions, when x=-1:

2x^{2}-x-2

Answer:

\\2x^2 - x - 2 \\= 2\times ( -1 )^2 - ( -1 ) - 2 \\ = 2 + 1 - 2 \\= 1

So the value at x=-1 is 1

Question:4(i) If a=2,b=-2,  find the value of:

  a^{2}+b^{2}

Answer:

a2 + b2

= ( 2 )2 + ( -2 )2 

= 4 + 4

= 8

If a = 2 and b = -2 the value of a2 + b2 = 8

Question:4(ii) If a=2,b=-2, find the value of:

  a^{2}+ab+b^{2}

Answer:

\\a^2 + ab + b^2 \\= 2^2 + 2 \times ( -2 ) + ( -2 )^2 \\= 4 - 4 + 4 \\= 4

If a = 2 and b = -2 the value of a2 + ab + b2 = 4

Question:4(iii) If a=2,b=-2,  find the value of 

a^{2}-b^{2}

Answer:

a2 - b2

= 22 - ( -2 )2

= 4 - 4

= 0

If a = 2 and b = -2 the value of a2 - b= 0

Question:5(i) When a=0,b=-1, find the value of the given expressions:

     2a+2b

Answer:

\\2a + 2b \\= 2 \times 0 + 2 \times ( -1 ) \\= 0 - 2 \\= -2

When a = 0 and b = -1 the value of the given expression 2a + 2b = -2

Question:5(ii) When a=0,b=-1, find the value of the given expressions:

 2a^{2}+b^{2}+1

Answer:

\\2a^2 + b^2 + 1 \\= 2 \times 0^2 + ( -1 )2 + 1 \\= 0 + 1 + 1 \\= 2

When a = 0 and b = -1 the value of the given expression 2a2 + b2 + 1 = 2

Question:5(iii) When a=0,b=-1 , find the value of the given expressions:

  2a^{2}b+2ab^{2}+ab

Answer:

\\2a^2b + 2ab^2 + ab \\= 2 \times 0^2 \times ( -1 ) + 2 \times 0 \times ( -1 )^2 + 0 \times ( -1 )\\ = 0 + 0 + 0 \\= 0

When a = 0 and b = -1 the value of the given expression 2a2b + 2ab2 + ab = 0

Question:5(iv) When a=0,b=-1, find the value of the given expressions:

 a^{2}+ab+2

Answer:

\\a^2 + ab + 2 \\= 0^2 + 0 \times ( -1 ) + 2 \\= 0 + 0 + 2 \\= 2

When a = 0 and b = -1 the value of the given expression a2 + ab + 2 = 2

Question:6(i) Simplify the expressions and find the value if x is equal to 2

  x+7+4(x-5)

Answer:

\\x + 7 + 4( x - 5 ) \\= x + 7 + 4x - 20 \\= 5x - 13 \\= 5 \times 2 - 13 \\= 10 - 13 \\= -3

If x is equal to 2 the value of x + 7 + 4( x - 5 ) = -3

Question:6(ii) Simplify the expressions and find the value if x is equal to 2

 3(x+2)+5x-7

Answer:

\\3( x + 2 ) + 5x - 7 \\= 3x + 6 + 5x - 7 \\= 8x - 1 \\= 8 \times (2) - 1 \\= 16 - 1 \\= 15

If x is equal to 2 the value of 3( x + 2 ) + 5x - 7 = 15

Question:6(iii) Simplify the expressions and find the value if x is equal to 2

 6x+5(x-2)

Answer:

\\6x + 5( x - 2 ) \\= 6x + 5x - 10 \\= 11x - 10 \\= 11 \times 2 - 10 \\= 22 - 10 \\= 12

If x is equal to 2 the value of  6x + 5( x - 2 ) = 12

Question:6(iv) Simplify the expressions and find the value if x is equal to 2 

 4(2x-1)+3x+11

Answer:

\\4( 2x - 1 ) + 3x + 11 \\= 8x - 4 + 3x + 11 \\= 11x + 7 \\= 11 \times 2 + 7 \\= 22 + 7 \\= 29

If x is equal to 2 the value of 4( 2x - 1 ) + 3x + 11 = 29

Question:8(i) If z=10,  find the value of 

z^{3}-3(z-10)

Answer:

\\z^3 - 3( z - 10 ) \\= z^3 - 3z + 30 \\= 10^3 - 3 \times 10 + 30 \\= 1000 - 30 + 30 \\= 1000

If z = 10 the value of z3 - 3( z - 10 ) = 1000

Question:8(ii) If p=-10, find the value of 

p^{2}-2p-100

Answer:

\\p^2 - 2p - 100 \\= ( -10 )^2 - 2 \times ( -10 ) - 100 \\= 100 + 20 - 100 \\= 20

If p = -10 the value of p2 - 2p - 100 = 20

Question:9 What should be the value of a if the value of 2x^{2}+x-a equals to 5, when 

x=0?

Answer:

\\2x^2 + x - a = 5 \\2 \times 0^2 + 0 - a = 5 \\-a = 5 \\a = -5

Therefore for a = -5 when the value of x=0

Question:10 Simplify the expression and find its value when a=5 and 

b=-3\; .2(a^{2}+ab)+3-ab

Answer:

\\2( a^2 + ab ) + 3 - ab \\= 2a^2 + 2ab + 3 - ab \\= 2a^2 + ab + 3 \\= 2 \times 5^2 + 5 \times ( -3 ) + 3 \\= 50 - 15 + 3 \\= 38

When a = 5 and b = -3 the value 2( a2 + ab ) + 3 - ab = 38

NCERT Solutions for Class 7 Maths- Chapter-wise 

Chapter No.

Chapter Name

Chapter 1

Solutions of NCERT for class 7 maths chapter 1 Integers

Chapter 2

CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals

Chapter 3

NCERT solutions for class 7 maths chapter 3 Data Handling

Chapter 4

Solutions of NCERT for class 7 maths chapter 4 Simple Equations

Chapter 5

CBSE NCERT solutions for class 7 maths chapter 5 Lines and Angles

Chapter 6

NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties

Chapter 7

Solutions of NCERT for class 7 maths chapter 7 Congruence of Triangles

Chapter 8 NCERT solutions for class 7 maths chapter 8 comparing quantities

Chapter 9

CBSE NCERT solutions for class 7 maths chapter 9 Rational Numbers

Chapter 10

NCERT solutions for class 7 maths chapter 10 Practical Geometry

Chapter 11

Solutions of NCERT for class 7 maths chapter 11 Perimeter and Area

Chapter 12

CBSE NCERT solutions for class 7 maths chapter 12 Algebraic Expressions

Chapter 13

NCERT solutions for class 7 maths chapter 13 Exponents and Powers

Chapter 14

Solutions of NCERT for class 7 maths chapter 14 Symmetry

 NCERT Solutions for Class 7- Subject-wise 

Solutions of NCERT for class 7 maths

CBSE NCERT solutions for class 7 science

Benefits of NCERT solutions for class 7 maths chapter 12 Algebraic Expressions-

  • You will learn to simplify and solve algebraic expressions in this chapter.
  • You will also learn the addition and subtraction of algebraic expressions which is helpful in making the expression simpler.
  • It will help you in your homework as all the NCERT questions including practice questions given below every topic are covered in this article.
  • There are many questions given below every topic to give you conceptual clarity. In NCERT solutions for class 7 maths chapter 12 algebraic expressions, you will get solutions to these practice questions also. 
  • You should practice all the NCERT questions including examples. If you facing difficulties in doing so, you can take help from these solutions.

Happy learning!!!

 

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