NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

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Written by Team Trustudies
Updated at 2021-02-11


NCERT solutions for class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1

Q.1 Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
(i) Subtraction of z from y.
(ii) One half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) Y- Z
(ii) 12 X+Y
(iii) Z×Z = Z2
(iv) 14pq
(v) x2+Y2
(vi) 3mm + 5
(vii) 10 – yz
(viii) ab – (a + b)

Q.2 (i) Identify the terms and their factors in the following expressions show the terms and factors by tree diagrams.
(a) x – 3
(b) 1+x+x2
(c) yy3
(d)5xy2+7x2y
(e) ?ab+2b23a2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(a) Expression: ( x-3 )
Term I = x
Term II = -3
(b) Expression: 1+x+x2
Term I = 1
Term II = x
Term III = x2 = x × x
(c) Expression: yy3
Term I = y
Term II = ?y3 = -y × -y ×-y
(d) Expression: 5xy2+7x2y
Term I = 5xy2 = 5×x×y×y
Term II = 7x2y = 7× x × x × y
(e) Expression: ?ab+2b23a2
Term I = -ab = -a × b
Term II = 2b2 = 2 × b × b
Term III = ?3a2 = -3 ×a×a

Q.2 (ii) Identify terms and factors in the expression given below:
(a) -4x + 5
(b) -4x + 5y
(c) 5y+3y2
(d)xy+2x2y2
(e) pq + q
(f) 1.2ab – 2.4b + 3.6a
(g) 34x+14
(h) 0.1p2+0.2q2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

Q.3 Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i)53t2
(ii)1+t+t2+t3
(iii)x+2xy+3y
(iv) 100m+1000n
(v) p2q2+7pq
(vi)1.2a+0.8b
(vii)3.14r2
(viii)2(l+b)
(ix)0.1y+0.01y2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

Q.4 (a) Identify terms which contain x and give the coefficient of x.
(i)y2x+y
(ii) 13y28yx
(iii) x+y+2
(iv)5+z+zx
(v) 1+x+xy
(vi)12xy2+25
(vii) 7x+xy2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) Expression: y2x+y
Term: y2x
Coefficient of x = y2
(ii) Expression: 13y28yx
Term: 8yx
Coefficient of x = 8y
(iii) Expression: x+y+2
Term: x
Coefficient of x = 1
(iv) Expression:5+z+zx
Term: zx
Coefficient of x = z
(v)Expression:1+x+xy
Term I x
Term II xy
Coefficient of x = 1, y
(vi) Expression:12xy2+25
Term: 12xy2
Coefficient of x = 12y2
(vii) Expression:7x+xy2
Term I 7x
Term II xy2
Coefficient of x = 7,y2

Q.4 (b) Identify terms which contain y2and give the coefficients ofy2.
(i) 8xy2
(ii) 5y2+7x
(iii) 2x2y15xy2+7y2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) Expression: 8xy2
Term : ?xy2
Coefficient ofy2=?x
(ii) Expression: 5y2+7x
Term : 5y2
Coefficient ofy2=5
(iii) Expression: 2x2y15xy2+7y2
Term : 15xy2,7y2
Coefficient ofy2=?15x,7

Q.5 Classify into monomials, binomials and trinomials: (i) 4y – 7x
(ii)y2
(iii) x + y – xy
(iv) 100
(v) ab – a – b
(vi) 5 – 3t
(vii) 4p2q4pq2
(viii) 7mn
(ix)z23z+8
(x) a2+b2
(xi)z2+z
(xii) 1+x+x2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) 4y – 7x __ Binomial
(ii)y2__ Monomial
(iii) x + y – xy__ Trinomial
(iv) 100__Monomial
(v) ab – a – b__Trinomial
(vi) 5 – 3t__Binomial
(vii) 4p2q4pq2__ Binomial
(viii) 7mn__Monimial
(ix)z23z+8__Trinomial
(x) a2+b2 __ Binomial
(xi)z2+z__Binomial
(xii) 1+x+x2__ Trinomial

Q.6 State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) -7x, 52x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v)4m2p,4mp2
(vi) 12xz,12x2y2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) 1, 100 like
(ii) -7x, 52x like
(iii) -29x, -29y unlike
(iv) 14xy, 42yx like
(v)4m2p,4mp2 unlike
(vi) 12xz,12x2y2 unlike

Q.7 Identify like terms in the following:
(a)?xy2,?4yx2,8x2,2xy2,7y2,?11x2,
?100x,?11yx,20x2y,?6x2,y,2xy,3x
(b)10pq,7p,8q,?p2q2,?7qp,?100q,?23,12q2p2,
?5p2,41,2405p,78qp,13p2q,qp2,701p2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(a) (i)xy2,2xy2
(ii)4yx2,20x2y
(iii)8x2,11x2,6x2
(iv)7y,y
(v) – 100x, 3x
(vi) – 11yx, 2xy (b)(i) 10pq, – 7qp, 78qp
(ii) 7p, 2405p
(iii) 8q, – 100q
(iv) p2q2,12q2p2
(v) – 23, 41
(vi) 5p2,701p2
(vii) 13p2q,qp2

NCERT solutions for class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.2

Q.1 Simplify combining like terms:
(i) 21b -32 + 7b- 20b
(ii) ?z2+13z2?5z+7z315z
(iii)p(pq)q(qp)
(iv) 3a – 2b — ab – (a – b + ab) + 3ab + 6 – a
(v)5x2y5x2+3yx23y2+x2y2+8xy2?3y2
(vi)(3y2+5y4)(8yy24)



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) 21b – 32 + 7b – 20b
= 21b + 7b -20b -32
= 8b -32
(ii) ?z2+13z2?5z+7z315z
= ?z2+13z2?5z?15z+7z3
= 11z2?20z+7z3
(iii) ( p – (p – q) – q – (q – p)
= p-p +q-q-q+p
= p- q
(iv) 3a – 2b — ab – (a – b + ab) + 3ab + 6 – a
= 3a - 2b - ab - a + b - ab +3ab + 6 - a
= 3a – a – a – 2b + b + b – ab – ab + 3ab
= a +ab
(v) 5x2y5x2+3yx23y2+x2y2+8xy2?3y2
= 5x2y+3yx25x2+x23y2y23y2+8xy2
= 8x^2y – 4x^2 – 7y^2 + 8xy^2
(vi) (3y2+5y4)(8yy24)
= 3y2+5y48y+y2+4)
= 3y2+y2+5y8y4+4
= 4y23y

Q.2 Add:
(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)4x2y,?3xy2,?5xy2,5x2y
(viii)3p2q24pq+5,?10p2q2,15+9pq+7p2q2
(ix) ab – 4a, 4b – ab, 4a – 4b
(x)x2y21,y21x2,1x2y2



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i) 3mn, -5mn, 8mn, -4mn
= (3 mn) + (-5 mn) + (8 mn) + (- 4 mn)
= 3 mn - 5 mn + 8 mn - 4 mn
= 2mn
(ii) t – 8tz, 3tz – z, z – t
= t – 8tz + 3tz – z + z – t
= t – t – 8tz + 3tz – z + z
= – 5 tz
(iii) -7mn + 5, 12mn + 2, 9mn – 8, -2mn – 3
= -7mn + 5 + 12mn + 2 + 9mn – 8 + (-2mn) – 3
= -7mn + 12 mn + 9mn – 2 mn + 5 + 2 – 8 – 3
= 12 mn – 4
(iv) a + b – 3, b – a + 3, a – b + 3
= a + b – 3 + b – a + 3 + a – b + 3
= a – a + a + b + b – b – 3 + 3 + 3
= a + b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
= 14x + 14y – 12xy – 13 + 18 – 7x – 10y + 8xy + 4xy
= -12xy + 8xy + 4xy + 14x – 7x + 10y – 10y – 13 + 18
= 0 + 7x + 0 + 5
= 7x + 5
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
= 5m -7n + 3n — 4m + 2 + 2m – 3mn – 5
= 5m – 4m + 2m – 7n + 3n- 3mn + 2 – 5
= 3m – 4n – 3mn – 3
(vii)4x2y,?3xy2,?5xy2,5x2y
= 4x2y+(?3xy2)+(?5xy2)+5x2y
=4x2y+5x2y3xy25xy2
=9x2y8xy2
(viii)3p2q24pq+5,?10p2q2,15+9pq+7p2q2
=3p2q24pq+5+(?10p2q2)+15+9pq+7p2q2
=3p2q210p2q2+7p2q24pq+9pq+5+15
= 5pq + 20
(ix) ab – 4a, 4b – ab, 4a – 4b
= ab – 4a + (4b – ab) + (4a – 4b)
= ab – 4a + 4b – ab + 4a – 4b
= ab – ab – 4a + 4a + 4b – 4b
= 0
(x)x2y21,y21x2,1x2y2
=x2y21+(y21x2)+(1x2y2)
=x2y21+y21x2+1x2y2
=x2x2x2y2+y2y211+1
=?x2y2?1

Q.3 Subtract:
(i)?5y2fromy2
(ii)6xyfrom?12xy
(iii)(ab)from(a+b)
(iv)a(b5)fromb(5a)
(v)?m2+5mnfrom4m23mn+8
(vi)?x2+10x5from5x10
(vii)5a27ab+5b2from3ab2a22b2
(viii)4pq5q23p2from5p2+3q2pq



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(i)?5y2fromy2
=y2(?5y2)
=y2+5y2
=6y2
(ii)6xyfrom?12xy
= -12xy – 6xy
= – 18xy
(iii)(ab)from(a+b)
= (a + b) – (a – b)
= a + b – a + b
= a – a + b + b
= 2b
(iv)a(b5)fromb(5a)
= b (5 -a) – a (b – 5)
= 5b – ab – ab + 5a
= 5a + 5b – 2ab
(v)?m2+5mnfrom4m23mn+8
=4m23mn+8(?m2+5mn)
=4m23mn+8+m25mn
=4m2+m23mn5mn+8
=5m28mn+8
(vi)?x2+10x5from5x10
=5x10(?x2+10x5)
=5x10+x210x+5
=x2+5x10x10+5
=x25x5
(vii)5a27ab+5b2from3ab2a22b2
=3ab2a22b2(5a27ab+5b2)
=3ab2a22b25a2+7ab5b2
=3ab+7ab2a25a22b25b2
=10ab7a27b2
(viii)4pq5q23p2from5p2+3q2pq
=5p2+3q2pq(4pq5q23p2)
=5p2+3q2pq4pq+5q2+3p2
=5p2+3p2+3q2+5q2pq4pq
=8p2+8q25pq

Q.4 (a) What should be added to x2+xy+y2 to obtain 2x2+3xy?
(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(a) p+(x2+xy+y2)=2x2+3xy
p=(2x2+3xy)(x2+xy+y2)
p=2x2+3xyx2xyy2
p=2x2x2+3xyxyy2
p=x2+2xyy2
(b) 2a + 8b + 10 – m = -3a + 7b + 16
m = (2a + 8b + 10) – (-3a + 7b + 16)
m = 2a + 8b + 10 + 3a – 7b – 16
m = 2a + 3a + 8b – 7b + 10 – 16
m = 5a + b – 6

Q.5 What should be taken away from3x24y2+5xy+20to obtain x2y2+6xy+20?



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

3x24y2+5xy+20m=?x2y2+6xy+20
m=3x24y2+5xy+20(?x2y2+6xy+20)
m=3x24y2+5xy+20+x2+y26xy20
m=3x2+x24y2+y2+5xy6xy+2020
m=4x23y2xy

Q.6 (a) From the sum of 3x – y + 11 and -y – 11, subtract 3x – y – 11.
(b) From the sum of 4 + 3x and54x+2x2,subtract the sum of 3x25x and?x2+2x+5.



NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions


Answer :

(a) sum of 3x – y + 11 and -y – 11
= 3x – y + 11 + (-y – 11)
= 3x – y + 11 – y – 11
= 3x – y – y + 11 – 11
= 3x – 2y
Now, subtract 3x – y – 11 from 3x – 2y = 3x – 2y – (3x – y – 11)
= 3x – 2y – 3x + y + 11
= 3x – 3x – 2y + y + 11
= -y + 11
(b) sum of 4 + 3x and54x+2x2,
=4+3x+(54x+2x2)
=4+3x+54x+2x2
=4+5+3x4x+2x2
=9x+2x2