# 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. Here you will get solutions to four exercises of this chapter.

Exercise:12.1

Exercise:12.2

Exercise:12.3

Exercise:12.4

## 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.

## Question: Describe how the following expressions are obtained:

$7xy+5, x^{2} y,4x^{2}-5x$

$7xy+5$

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

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

$8y+3x^{2}$ 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

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

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

$4x-3y,a+b+5,2y+5,2xy$

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$$-25y$$1$$x$$12y$$y$

The like terms are grouped below

Group 1: $12x$$-25x$$x$

Group 2: $-25y$$12y$$y$

Group 3: $12$$-25$$1$

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

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

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

Subtraction of $z$ from $y$.

Subtraction of z from y: $y-z$

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

Sum of numbers x and y = x + y

One half of the sum of numbers x and y

$=\frac{x+y}{2}$

The number $z$ multiplied by itself.

The number $z$ multiplied by itself $=z\times z=z^{2}$

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

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

One-fourth of the product of numbers p and q

$=\frac{pq}{4}$

Numbers $x$ and $y$ both squared and added.

Number x squared =$x^{2}$

Number y squared = $y^{2}$

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

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

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

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

Product of numbers $y$ and $z$ subtracted from $10$.

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

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

Sum of numbers $a$ and $b$ subtracted from their product.

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 $= ab - (a+b) = ab - a - b$.

Expression : x - 3

Terms in the above expression: x and -3

Tree diagram for the given expression

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

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

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

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

(a)  $-4x+5$

Expression: -4x + 5

Terms in the above expression: -4x and 5

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

Factors of 5: 5

(b)  $-4x+5y$

Expression: -4x + 5y

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

Factors of  -4x: -1, 4 and x

Factors of 5y: 5 and y

(c)  $5y+3y^{2}$

Expression: 5y + 3y2

Terms in the above expression: 5y and 3y2

Factors of  5y: 5 and y

Factors of 3y2: 3, y and y

(d)  $xy+2x^{2}y^{2}$

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

(e)  $pq+q$

Expression: pq + q

Tems in the above expression: pq and q

Factors of  pq: p and q

Factors of q: q

(f)  $1.2 \; ab-2.4\; b+3.6\; a$

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

(g)  $\frac{3}{4}x+\frac{1}{4}$

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  $\frac{1}{4}$:   $\frac{1}{4}$

(h)  $0.1\; p^{2}+0.2\; q^{2}$

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

$5-3t^{2}$

Expression: 5 - 3t2

Tems in the above expression: 5 and -3t2

Coefficient of -3t2: -3

$1+t+t^{2}+t^{3}$

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

$x+2xy+3y$

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

$100m+1000n$

Expression: 100m + 1000n

Terms in the above expression: 100m and 1000n

Coefficient of 100m: 100

Coefficient of 1000n: 1000

$-p^{2}q^{2}+7pq$

Expression: -p2q2 + 7pq

Tems in the above expression: -p2q2 and 7pq

Coefficient of -p2q2: -1

Coefficient of 7pq: 7

$1.2\; a+0.8\; b$

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

$3.14\; r^{2}$

Expression: 3.14r2

Terms in the above expression: 3.14r2

Coefficient of 3.14ris 3.1

$2(l+b)$

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

Tems in the above expression: 2l and 2b

Coefficient of 2l: 2

Coefficient of 2b: 2

$0.1\; y+0.01\; y^{2}$

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

(i)  $y^{2}x+y$

Expression: y2x + y

Terms with x: y2x

Coefficient of x in y2x: y2

(ii)  $13y^{2}-8yx$

Expression: 13y2 - 8yx

Terms with x: -8yx

Coefficient of x in -8yx: -8y

(iii) $x+y+2$

Expression: x + y + 2

Terms with x: x

Coefficient of x in x: 1

(iv)  $5+z+zx$

Expression: 5 + z + zx

Terms with x: zx

Coefficient of x in zx: z

(v)  $1+x+xy$

Expression: 1 + x + xy

Terms with x: x and xy

Coefficient of x in x: 1

Coefficient of x in xy: y

(vi)  $12xy^{2}+25$

Expression: 12xy2 + 5

Terms with x: 12xy2

Coefficient of x in 12xy2: 12y2

(vii)  $7x+xy^{2}$

Expression: 7x + xy2

Terms with x: 7x and xy2

Coefficient of x in 7x: 7

Coefficient of x in xy2: y2

Expression: 8 - xy2

Terms with y2: -xy2

Coefficient of y2 in -xy2: -x

Expression: 5y2 + 7x

Terms with y2: 5y2

Coefficient of y2 in 5y2: 5

(iii)  $2x^{2}y-15xy^{2}+7y^{2}$

Expression: 2x2y -15xy2 + 7y2

Terms with y2: -15xy2 and 7y2

Coefficient of y2 in -15xy2: -15x

Coefficient of y2 in 7y2: 7

(i) 4y – 7z

(ii) y2

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p2q – 4pq2

(viii) 7mn

(ix) z2 – 3z + 8

(x) a2 + b2

(xi) z2 + z

(xii) 1 + x + x2

(i) 4y – 7z

Binomial

(ii) y2

Monomial

(iii) x + y – xy

Trinomial

(iv) 100

Monomial

(v) ab – a – b

Trinomial

(vi) 5 – 3t

Binomial

(vii) 4p2q – 4pq2

Binomial

(viii) 7mn

Monomial

(ix) z2 – 3z + 8

Trinomial

(x) a2 + b2

Binomial

(xi) z2 + z

Binomial

(xii) 1 + x + x2

Trinomial

$1,100$

(i)  $1,100$ are Like terms.

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

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

$-29x, -29y$

Unlike since y and x are unlike terms

$14xy,42yx$

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

$4m^{2}p,4mp^{2}$

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

$12xz,12x^{2}z^{2}$

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

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

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

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:

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

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

$m-n,m+n$

$m-n,m+n$

Will give the result as follows

$m-n+m+n=2m$

Subtracting

$m-n,m+n$

Will give the result as follows

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

$mn+5-2,mn+3$

$mn+5-2,mn+3$

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:

$21b-32+7b-20b$

21b - 32 + 7b -20b

= (21 + 7 - 20)b -32

= 8b - 32

The simplified expression is 8b - 32.

Question:1(ii) Simplify combining like terms:

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

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

-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:

$p-(p-q)-q-(q-p)$

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:

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

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:

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

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:

$(3y^{2}+5y-4)-(8y-y^{2}-4)$

(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

(i)  $3mn,-5mn,8mn,-4mn$

(ii)  $t-8tz,3tz-z,z-t$

(iii) $-7mn+5,12mn+2,9mn-8,-2mn-3$

(iv) $a+b-3,b-a+3,a-b+3$

(v)  $14x+10y-12xy-13,18-7x-10y+8xy,4xy$

vi)  $5m-7n,3n-4m+2,2m-3mn-5$

(vii)  $4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y$

(viii)  $3p^{2}q^{2}-4pq+5,-10 p^{2}q^{2},15+9pq+7p^{2}q^{2}$

(ix)  $ab-4a,4b-ab,4a-4b$

(x) $x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}$

The given terms are added as follows

$\\(i) 3mn + (-5mn) + 8mn + (-4mn)\\ = (3 - 5 + 8 - 4)mn\\ = 2mn$

$\\(ii) t - 8tz + (3tz - z) + (z - t)\\ = t - 8tz + 3tz - z + z - t\\ = (1 - 1)t + (-8 + 3)tz + (-1 + 1)z\\ = -5tz$

$\\(iii) -7mn + 5 + (12mn + 2) + (9mn - 8) + (-2mn - 3)\\ = -7mn + 5 + 12mn + 2 + 9mn - 8 - 2mn - 3 \\= (-7 + 12 + 9 - 2)mn + 5 + 2 - 8 - 3 \\= 12mn - 4$

$\\(iv) a + b - 3 + (b - a + 3) + (a - b + 3)\\ \\= a + b - 3 + b - a + 3 + a - b + 3 \\= (1 - 1 + 1)a + (1 + 1 -1)b - 3 + 3 + 3 \\= a + b + 3$

$\\(v) 14x + 10y - 12xy - 13 + (18 - 7x - 10y + 8xy) + 4xy\\ = 14x + 10y - 12xy - 13 + 18 - 7x - 10y + 8xy + 4xy \\= (14 -7)x + (10 - 10)y + (-12 + 8 + 4)xy - 13 + 18 \\= 7x + 5$

$\\(vi) 5m - 7n + (3n - 4m + 2) + (2m - 3mn - 5) \\= 5m - 7n + 3n - 4m + 2 + 2m - 3mn - 5 \\= (5 - 4 + 2)m + (-7 + 3)n + 2 - 5 - 3mn \\= 3m - 4n - 3mn - 3$

$\\(vii) 4x^2y - 3xy^2 - 5xy^2 + 5x^2y\\ \\= (4 + 5)x^2y + (-3 - 5)xy^2 \\= 9x^2y - 8xy^2$

$\\(viii) 3p^2q^2 - 4pq + 5 + (-10p^2q^2) + (15 + 9pq + 7p^2q^2) \\= 3p^2q^2 - 4pq + 5 - 10p^2q^2 + 15 + 9pq + 7p^2q^2 \\= (3 - 10 + 7)p^2q^2 + (-4 + 9)pq + 5 + 15 \\= 5pq + 20$

$\\(ix) ab - 4a + (4b - ab) + (4a - 4b) \\= ab - 4a + 4b - ab + 4a - 4b \\= (1 - 1)ab + (-4 + 4)a + (4 - 4)b \\=0$

$\\(x)\ x^2 - y^2 - 1 + (y^2 - 1 - x^2) + (1 - x^2 - y^2) \\= (1 - 1 - 1)x^2 + (-1 + 1 - 1)y^2 - 1 - 1 + 1 \\= -x^2 - y^2 - 1$

Question:3 Subtract:

(i)  $-5y^{2}$ from $y^{2}$

(ii) $6xy$ from $-12xy$

(iii) $(a-b)$ from $(a+b)$

(iv)   $a(b-5)$ from $b(5-a)$

(v)  $-m^{2}+5mn$ from $4m^{2}-3mn+8$

(vi)  $-x^{2}+10x-5$ from $5x-10$

(vii) $5a^{2}-7ab+5b^{2}$ from $3ab-2a^{2}-2b^{2}$

(viii) $4pq-5q^{2}-3p^{2}$ from $5p^{2}+3q^{2}-pq$

The given terms are subtracted as follows

(i)

$\\ y^2 - (-5y^2) \\= y^2 + 5y^2 \\= 6y^2$

(ii)

$\\ -12xy - 6xy\\ = -18xy$

(iii)

$\\(a+b)-(a-b)\\ =a+b-a+b =2b$

(iv)

$\\ b(5 - a) - a(b - 5) \\= 5b - ab - (ab - 5a) \\= 5b - ab - ab + 5a \\= 5b - 2ab + 5a$

(v)

$\\4m^2 - 3mn + 8 - (-m^2 + 5mn) \\= 4m^2 - 3mn + 8 + m^2 - 5mn \\= (4 + 1)m^2 + (-3 - 5)mn + 8 \\= 5m^2 - 8mn + 8$

(vi)

$\\ 5x - 10 - (-x^2 + 10x - 5) \\= 5x - 10 + x^2 - 10x + 5 \\= x^2 + (5 - 10)x - 10 + 5 \\= x^2 - 5x - 5$

(vii)

$\\ 3ab - 2a^2 - 2b^2 - (5a^2 - 7ab + 5b^2) \\= 3ab - 2a^2 - 2b^2 - 5a^2 + 7ab - 5b^2 \\= (3 + 7)ab + (-2 -5)a^2 + (-2 - 5)b^2 \\= 10ab - 7a^2 - 7b^2$
(viii)

$\\ 5p^2 + 3q^2 - pq - (4pq - 5q^2 - 3p^2) \\= 5p^2 + 3q^2 - pq - 4pq + 5q^2 + 3p^2 \\= (5 + 3) p^2 + (3 + 5)q^2 + (-1 - 4)pq \\= 8p^2 + 8q^2 - 5pq$

$2x^{2}+3xy?$

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

$-3a+7b+16 ?$

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

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

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

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

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

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

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

$m-2$

(i) m - 2

= 2 - 2

= 0

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

$3m-5$

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

If m = 2 the value of 3m - 5 = 1

$9-5m$

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

If m = 2 the value of 9 - 5m = -1

$3m^{2}-2m-7$

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

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

$\frac{5m}{2}-4$

$\frac{5m}{2}-4$

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

= 5 - 4

= 1

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

$4p+7$

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

If p = -2 the value of 4p + 7 = -1

$-3p^{2}+4p+7$

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

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

$-2p^{3}-3p^{2}+4p+7$

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

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

$2x-7$

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

If x = -1 the value of 2x - 7 = -9

$x^{2}+2x+1$

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

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

$2x^{2}-x-2$

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

So the value at x=-1 is 1

$a^{2}+b^{2}$

a2 + b2

= ( 2 )2 + ( -2 )2

= 4 + 4

= 8

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

$a^{2}+ab+b^{2}$

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

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

$a^{2}-b^{2}$

a2 - b2

= 22 - ( -2 )2

= 4 - 4

= 0

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

$2a+2b$

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

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

$2a^{2}+b^{2}+1$

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

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

$2a^{2}b+2ab^{2}+ab$

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

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

$a^{2}+ab+2$

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

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

$x+7+4(x-5)$

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

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

$3(x+2)+5x-7$

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

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

$6x+5(x-2)$

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

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

$4(2x-1)+3x+11$

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

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

$x=3,a=-1,b=-2.$

(i)  $3x-5-x+9$

(ii)  $2-8x+4x+4$

(iii)  $3a+5-8a+1$

(iv) $10-3b-4-5b$

(v)  $2a-2b-4-5+a$

The expression is simplified as follows and also obtained their values

(i)

$\\ 3x - 5 - x + 9 \\= 2x + 4 \\= 2 \times 3 + 4 \\= 10$

(ii)

$\\ 2 - 8x + 4x + 4 \\= 6 - 4x \\= 6 - 4 \times 3 \\= -6$

(iii)

$\\3a + 5 - 8a + 1 \\= -5a + 6 \\= -5 \times ( -1 ) + 6 \\= 5 + 6 \\=11$

(iv)

$\\10 - 3b - 4 - 5b \\= 6 - 8b \\= 6 - 8 \times ( -2 ) \\= 6 + 16 \\= 22$

(v)

$\\2a - 2b - 4 - 5 + a \\= 3a - 2b - 9 \\= 3 \times ( -1 ) - 2 \times ( -2 ) - 9 \\= -3 + 4 - 9 \\= -8$

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

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

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

$p^{2}-2p-100$

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

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

$x=0?$

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

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

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

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

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

## Solutions of NCERT for class 7 maths chapter 12 algebraic expression-Exercise: 12.4

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind

The number of segments required to form n of each digits shown above are 5n + 1, 3n + 1 and 5n + 2

When n = 5

$\\5n + 1 = 5 \times 5 + 1 = 26 \\3n + 1 = 3 \times 5 + 1 = 16 \\5n + 2 = 5 \times 5 + 2 = 27$

When n = 10

$\\5n + 1 = 5 \times 10 + 1 = 51 \\3n + 1 = 3 \times 10+ 1 = 31 \\5n + 2 = 5 \times 10 + 2 = 52$

When n = 100

$\\5n + 1 = 5 \times 100 + 1 = 501 \\3n + 1 = 3 \times 100+ 1 = 301 \\5n + 2 = 5 \times 100 + 2 = 502$

Below you can find the table of number patterns:

## 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

## 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.
• 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!!!