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
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.
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.
Answer:
the above expression is obtained by adding 7xy with 5. Here 7xy is obtained by multiplying 7,x and y
the above expression is obtained by subtracting the product of 5 and x from the product of 4,x and x
Answer:
The terms in the expression are
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
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.
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
Question: Identify the coefficients of the terms of following expressions:
Answer:
i) 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
Question:1(i) Group the like terms together from the following:
Answer:
The like terms are grouped below
Group 1: , ,
Group 2: , ,
Group 3: , ,
Question: Classify the following expressions as a monomial, a binomial or a trinomial:
Answer:
Monomial: a, xy, 7
binomial: a+b, xy+5, 4mn+7
Trinomial: ab+a+b, 5x^{2}x+2, 4pq3q+5p, 4m7n+10
Polynomial with 4 terms: ab+a+b5
Question:1(i) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
Answer:
Subtraction of z from y:
Question:1(ii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation.
Onehalf of the sum of numbers and .
Answer:
Sum of numbers x and y = x + y
One half of the sum of numbers x and y
Question:1(iii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
The number multiplied by itself.
Answer:
The number multiplied by itself
Question:1(iv) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
Onefourth of the product of numbers and .
Answer:
Product of the numbers p and q
Onefourth of the product of numbers p and q
Question:1(v) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
Numbers and both squared and added.
Answer:
Number x squared =
Number y squared =
Numbers x and y both squared and added =
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 and .
Answer:
Product of numbers m and n
Number 5 added to three times the product of numbers and =
Question:1(vii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
Product of numbers and subtracted from .
Answer:
Product of numbers y and z
Product of numbers y and z subtracted from 10
Question:1(viii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
Sum of numbers and subtracted from their product.
Answer:
Sum of numbers a and b = a + b
Product of the numbers a and b
Sum of numbers and subtracted from their product .
Question:2(i) Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams. (a)
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)
Answer:
Expression:
Tems in the above expression:
Factors of x^{2}: 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)
Answer:
Expression: y  y^{3}
Tems in the above expression: y and y^{3}
Factors of y^{3}: 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)
Answer:
Expression: 5xy^{2} + 7x^{2}y
Terms in the above expression: 5xy^{2} and 7x^{2}y
Factors of 5xy^{2}: 5, x, y and y
Factors of 7x^{2}y: 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)
Answer:
Expression: ab + 2ab^{2}  3a^{2}
Terms in the above expression: ab, 2ab^{2} and 3a^{2}
Factors of ab: 1, a and b
Factors of 2ab^{2}: 2, a, b and b
Factors of 3a^{2}: 1, 3, a and a
Tree diagram for the given expression
Question:2(ii) Identify terms and factors in the expressions given below:
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:
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:
Answer:
Expression: 5y + 3y^{2}
Terms in the above expression: 5y and 3y^{2}
Factors of 5y: 5 and y
Factors of 3y^{2}: 3, y and y
Question:2(ii) Identify terms and factors in the expressions given below:
Answer:
Expression: xy + 2x^{2}y^{2}
Terms in the above expression: xy and 2x^{2}y^{2}
Factors of xy: x and y
Factors of 2x^{2}y^{2}: 2, x, x, y and y
Question:2(ii) Identify terms and factors in the expressions given below:
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:
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:
Answer:
Expression:
Terms in the above expression: and
Factors of : and x
Factors of :
Question:2(ii) Identify terms and factors in the expressions given below:
Answer:
Expression: 0.1p^{2} + 0.2q^{2}
Tems in the above expression:0.1p^{2} and 0.2q^{2}
Factors of 0.1p^{2}: 0.1, p and p
Factors of 0.2q^{2}: 0.2, q and q
Question:3(i) Identify the numerical coefficients of terms (other than constants) in the following expressions:
Answer:
Expression: 5  3t^{2}
Tems in the above expression: 5 and 3t^{2}
Coefficient of 3t^{2}: 3
Question:3(ii) Identify the numerical coefficients of terms (other than constants) in the following expressions:
Answer:
Expression: 1 + t + t^{2} + t^{3}
Terms in the above expression: 1, t, t^{2} and t^{3}
Coefficient of t is 1
Coefficient of t^{2 } is 1
Coefficient of t^{3}: is 1
Question:3(iii) Identify the numerical coefficients of terms (other than constants) in the following expressions:
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:
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:
Answer:
Expression: p^{2}q^{2} + 7pq
Tems in the above expression: p^{2}q^{2} and 7pq
Coefficient of p^{2}q^{2}: 1
Coefficient of 7pq: 7
Question:3(vi) Identify the numerical coefficients of terms (other than constants) in the following expressions:
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:
Answer:
Expression: 3.14r^{2}
Terms in the above expression: 3.14r^{2}
Coefficient of 3.14r^{2 }is 3.1
Question:3(viii) Identify the numerical coefficients of terms (other than constants) in the following expressions:
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:
Answer:
Expression: 0.1y + 0.01y^{2}
Tems in the above expression: 0.1y and 0.01y^{2}
Coefficient of 0.1y is 0.1
Coefficient of 0.01y^{2 } is 0.01
Question:4(a) Identify terms which contain x and give the coefficient of x.
Answer:
Expression: y^{2}x + y
Terms with x: y^{2}x
Coefficient of x in y^{2}x: y^{2}
Question:4(a) Identify terms which contain x and give the coefficient of x.
Answer:
Expression: 13y^{2}  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.
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.
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 .
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.
Answer:
Expression: 12xy^{2} + 5
Terms with x: 12xy^{2}
Coefficient of x in 12xy^{2}: 12y^{2}
Question:4(a) Identify terms which contain x and give the coefficient of x.
Answer:
Expression: 7x + xy^{2}
Terms with x: 7x and xy^{2}
Coefficient of x in 7x: 7
Coefficient of x in xy^{2}: y^{2}
Question:4(b) Identify terms which contain and give the coefficient of .
Answer:
Expression: 8  xy^{2}
Terms with y^{2}: xy^{2}
Coefficient of y^{2} in xy^{2}: x
Question:4(b) Identify terms which contain and give the coefficient of .
Answer:
Expression: 5y^{2} + 7x
Terms with y^{2}: 5y^{2}
Coefficient of y^{2} in 5y^{2}: 5
Question:4(b) Identify terms which contain and give the coefficient of .
Answer:
Expression: 2x^{2}y 15xy^{2} + 7y^{2}
Terms with y^{2}: 15xy^{2} and 7y^{2}
Coefficient of y^{2} in 15xy^{2}: 15x
Coefficient of y^{2} in 7y^{2}: 7
Question:5 Classify into monomials, binomials and trinomials.
Answer:
(i) 4y – 7z
Binomial
(ii) y^{2}
Monomial
(iii) x + y – xy
Trinomial
(iv) 100
Monomial
(v) ab – a – b
Trinomial
(vi) 5 – 3t
Binomial
(vii) 4p^{2}q – 4pq^{2}
Binomial
(viii) 7mn
Monomial
(ix) z^{2} – 3z + 8
Trinomial
(x) a^{2} + b^{2}
Binomial
(xi) z^{2} + z
Binomial
(xii) 1 + x + x^{2}
Trinomial
Question:6(i) State whether a given pair of terms is of like or unlike terms.
Answer:
(i) are Like terms.
Question:6(ii) State whether a given pair of terms is of like or unlike terms.
Answer:
(ii) are Like terms
Question:6(iii) State whether a given pair of terms is of like or unlike terms.
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.
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.
Answer:
Unlike since are different
Question:6(vi) State whether a given pair of terms is of like or unlike terms.
Answer:
Unlike since are unlike terms
Question:7(a) Identify like terms in the following:
Answer:
Like terms are
(i) xy^{2 }and 2xy^{2 }
(ii) 4x^{2}y and 20x^{2}y
(iii) 8x^{2}, 11x^{2} and 6x^{2}
(iv) 7y and y
(v) 100x and 3x
(vi) 11yx and 2xy
Question:7(b) Identify like terms in the following:
Answer:
Like terms are
(i) 10pq, 7qp and 78qp
(ii) 7p and 2405p
(iii) 8q and 100q
(iv) p^{2}q^{2} and 12q^{2}p^{2}
(vii) 23 and 41
(viii) 5p^{2} and 701p^{2}
(ix) 13p^{2}q and qp^{2}
Question:(i) Add and subtract
Answer:
Adding
Will give the result as follows
Subtracting
Will give the result as follows
Answer:
adding the following terms
we will get
Subtracting
We will get
Question:1(i) Simplify combining like terms:
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:
Answer:
z^{2} + 13z^{2}  5z + 7z^{3}  15z
= (1 + 13)z^{2} + (5  15)z +7z^{3}
=12z^{2}  20z + 7z^{3}
The simplified expression is 12z^{2}  20z + 7z^{3}
Question:1(iii) Simplify combining like terms:
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:
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:
Answer:
5x^{2}y  5x^{2} + 3yx^{2}  3y^{2} + x^{2}  y^{2} + 8xy^{2}  3y^{2}
= (5 + 3 )x^{2}y + (5 + 1)x^{2} + (3  1  3)y^{2} + 8xy^{2}
= 8x^{2}y  4x^{2}  7y^{2} + 8xy^{2}
The simplified expression is 8x^{2}y  4x^{2}  7y^{2} + 8xy^{2}
Question:1(vi) Simplify combining like terms:
Answer:
(3y^{2} + 5y  4)  (8y  y^{2}  4)
= 3y^{2} + 5y  4  8y + y^{2} + 4
= (3 + 1)y^{2} + (5  8)y  4 + 4
= 4y^{2}  3y
The simplified expression is 4y^{2}  3y
Question:3 Subtract:
Answer:
The given terms are subtracted as follows
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Question:4(a) What should be added to to obtain
Answer:
Let the term be a which must be added to x^{2} + xy + y^{2} to obtain 2x^{2} + 3xy
x^{2} + 2xy  y^{2 }should be added to x^{2} + xy + y^{2} to obtain 2x^{2} + 3xy
Question:4(b) What should be subtracted from to get
Answer:
Let the term be c which must be subtracted from 2a + 8b + 10 to get 3a + 7b + 16
5a + b  6 must be subtracted from 2a + 8b + 10 to get 3a + 7b + 16
Question:5 What should be taken away from to obtain
Answer:
Let the term be a which must be taken away from 3x^{2}  4y^{2} + 5xy + 20 to obtain x^{2}  y^{2} + 6xy + 20
4x^{2}  3y^{2}  xy must be taken away from 3x^{2}  4y^{2} + 5xy + 20 to obtain x^{2}  y^{2} + 6xy + 20
Question:6(a) From the sum of and, subtract
Answer:
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 and subtract the sum of and .
Answer:
On subtracting the sum of and from the sum of and we get
Question:1(i) If find the value of:
Answer:
(i) m  2
= 2  2
= 0
If m = 2 the value of m  2 = 0
Question:1(v) If find the value of: (v) If find the value of:
Answer:
= 5  4
= 1
If m = 2 the value of
Question:2(iii) If , find the value of:
Answer:
If p = 2 the value of 2p^{3}  3p^{2} + 4p + 7 = 3
Question:3(i) Find the value of the following expressions, when :
Answer:
If x = 1 the value of 2x  7 = 9
Question:3(ii)Find the value of the following expressions, when
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 :
Answer:
If x = 1 the value of x^{2} + 2x + 1 = 0
Question:3(iv) Find the value of the following expressions, when :
Answer:
So the value at x=1 is 1
Question:4(i) If find the value of:
Answer:
a^{2} + b^{2}
= ( 2 )^{2} + ( 2 )^{2}
= 4 + 4
= 8
If a = 2 and b = 2 the value of a^{2} + b^{2} = 8
Question:4(ii) If find the value of:
Answer:
If a = 2 and b = 2 the value of a^{2} + ab + b^{2} = 4
Question:4(iii) If find the value of
Answer:
a^{2}  b^{2}
= 2^{2}  ( 2 )^{2}
= 4  4
= 0
If a = 2 and b = 2 the value of a^{2}  b^{2 }= 0
Question:5(i) When find the value of the given expressions:
Answer:
When a = 0 and b = 1 the value of the given expression 2a + 2b = 2
Question:5(ii) When find the value of the given expressions:
Answer:
When a = 0 and b = 1 the value of the given expression 2a^{2} + b^{2} + 1 = 2
Question:5(iii) When , find the value of the given expressions:
Answer:
When a = 0 and b = 1 the value of the given expression 2a^{2}b + 2ab^{2} + ab = 0
Question:5(iv) When find the value of the given expressions:
Answer:
When a = 0 and b = 1 the value of the given expression a^{2} + ab + 2 = 2
Question:6(i) Simplify the expressions and find the value if is equal to
Answer:
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 is equal to
Answer:
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 is equal to
Answer:
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 is equal to
Answer:
If x is equal to 2 the value of 4( 2x  1 ) + 3x + 11 = 29
Question:9 What should be the value of a if the value of equals to , when
Answer:
Therefore for a = 5 when the value of x=0
Question:10 Simplify the expression and find its value when and
Answer:
When a = 5 and b = 3 the value 2( a^{2} + ab ) + 3  ab = 38
Answer:
The number of segments required to form n of each digits shown above are 5n + 1, 3n + 1 and 5n + 2
When n = 5
When n = 10
When n = 100
Question:2 Use the given algebraic expression to complete the table of number patterns.
Answer:
Below you can find the table of number patterns:
Chapter No. 
Chapter Name 
Chapter 1 

Chapter 2 
CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals 
Chapter 3 

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 
Happy learning!!!