Algebraic Expressions - Solutions

 CBSE Class –VII Mathematics

NCERT Solutions
Algebraic Expressions (Ex. 12.1)


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

  1. Subtraction of z from y.
  2. One-half of the sum of numbers x and y.
  3. The number z multiplied by itself.
  4. One-fourth of the product of numbers p and q.
  5. Numbers x and y both squared and added.
  6. Number 5 added to three times the product of m and n.
  7. Product of numbers y and z subtracted from 10.
  8. Sum of numbers a and b subtracted from their product.

Answer: (i) yz

(ii) x+y2

(iii) z2

(iv) pq4

(v) x2+y2

(vi) 3mn+5

(vii) 10yz

(viii) ab(a+b)


Question 2.(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:

(a) x3

(b) 1+x+x2

(c) yy3

(d) 5xy2+7x2y

(e) ab+2b23a2

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

(a) 4x+5

(b) 4x+5y

(c) 5y+3y2

(d) xy+2x2y2

(e) pq+q

(f) 1.2ab2.4b+3.6a

(g) 34x+14

(h) 0.1p2+0.2q2

Answer: (i) (a) x3

(b) 1+x+x2

Expression

(c) yy3

Expression

(d) 5xy2+7x2y

Expression


(e) ab+2b23a2

Expression

(ii) (a) 4x+5

Terms: 4x,5

Factors: 4,x ; 5

(b) 4x+5y

Terms: 4x,5y

Factors: 4,x ; 5,y

(c) 5y+3y2

Terms: 5y,3y2

Factors: 5,y ; 3,y,y

(d) xy+2x2y2

Terms: xy,2x2y2

Factors: x,y ; 2x,x,y,y

(e) pq+q

Terms: pq,q

Factors: p,q ; q

(f) 1.2ab2.4b+3.6a

Terms: 1.2ab,2.4b,3.6a

Factors: 1.2,a,b ; 2.4,b ; 3.6,a

(g) 34x+14

Terms: 34x,14

Factors: 34,x ; 14

(h) 0.1p2+0.2q2

Terms: 0.1p2,0.2q2

Factors: 0.1,p,p ; 0.2,q,q


Question 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

Answer:

S.No.ExpressionTermsNumerical Coefficient
(i)53t23t23
(ii)1+t+t2+t3t1
t21
t31
(iii)x+2xy+3yx1
2xy2
3y3
(iv)100m+1000n100m100
1000n1000
(v)p2q2+7pqp2q21
7pq7
(vi)1.2a+0.8b1.2a1.2
0.8b0.8
(vii)3.14r23.14r23.14
(viii)2(l+b)=2l+2b2l2
2b2
(ix)0.1y+0.01y20.1y0.1
0.01y20.01

Question 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

(b) Identify terms which contain y2 and give the coefficient of y2.

(i) 8xy2

(ii) 5y2+7x

(iii) 2x2y15xy2+7y2

Answer: (a)

S.No.ExpressionTerm with factor xCoefficient of x
(i)y2x+yy2xy2
(ii)13y28yx8yx8y
(iii)x+y+2x1
(iv)5+z+zxzxz
(v)1+x+xyx1
xyy
(vi)12xy2+2512xy212y2
(vii)7x+xy2xy2y2
7x7

(b)

S.No.ExpressionTerm contains y2Coefficient of y2
(i)8xy2xy2x
(ii)5y2+7x5y25
(iii)2x2y15xy2+7y215xy215x
7y27

Question 5.Classify into monomials, binomials and trinomials:

(i) 4y7x

(ii) y2

(iii) x+yxy

(iv) 100

(v) abab

(vi) 53t

(vii) 4p2q4pq2

(viii) 7mn

(ix) z23z+8

(x) a2+b2

(xi) z2+z

(xii) 1+x+x2

Answer:

S.No.ExpressionType of Polynomial
(i)4y7zBinomial
(ii)y2Monomial
(iii)x+yxyTrinomial
(iv)100Monomial
(v)ababTrinomial
(vi)53tBinomial
(vii)4p2q4pq2Binomial
(viii)7mnMonomial
(ix)z23z+8Trinomial
(x)a2+b2Binomial
(xi)z2+zBinomial
(xii)1+x+x2Trinomial

Question 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,12x2z2

Answer:

S.No.Pair of termsLike / Unlike terms
(i)1, 100Like terms
(ii)7x,52xLike terms
(iii)29x,29yUnlike terms
(iv)14xy,42yxLike terms
(v)4m2p,4mp2Unlike terms
(vi)12xz,12x2z2Unlike terms

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

Answer: (a) Like terms are:
(i) xy2,2xy2
(ii) 4yx2,20x2y
(iii) 8x2,11x2,6x2
(iv) 7y,y
(v) 100x,3x
(vi) 11yx,2xy

(b) Like terms are:
(i) 10pq,7pq,78pq
(ii) 7p,2405p
(iii) 8q,100q
(iv) p2q2,12p2q2
(v) 12,41
(vi) 5p2,701p2
(vii)