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Chapter 12 Algebraic Expressions Ex 12.1 Solutions

Question - 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 2 subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.

Answer - 1 : -

(i) Subtraction of z from y
Expression: y – z

(ii)One half of the sum of numbers x and y
Expression: 1/2(x+y) or (x+y)/2

(iii) The number 2 multiplied by itself.
Expression: z × z = z2

(iv)One-fourth of the product of numbers p and q
Expression: (1/4)pq or pq/4

(v) Numbers x and y both squared and added
Expression: x2 + y2

(vi) Number 5 added to three times the product of number m and n
Expression: 3mn + 5

(vii) Product of numbers y and z subtracted from 10
Expression: 10 – yz

(viii) Sum of numbers a and 6 subtracted from their product
Expression: Sum = a + b, Product = ab
∴Required expression
= ab – (a + b)
= ab – a- b

Question - 2 : - Identify the terms and their factors in thefollowing expressions show the terms and factors by tree diagrams.
(a) x – 3
(b) 1 + x + x2
(c) y – y3
(d) 5xy2 + 7x2y
(e) -ab + 2b2 – 3a2

Answer - 2 : -


Question - 3 : - 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) (3/4)x+1/4
(h) 0.1p2 + 0.2q2

Answer - 3 : -


Question - 4 : - Identify the numerical coefficients of terms (otherthan constants) in the following:
(i) 5 – 3t2
(ii) 1 + t + t2 + t3
(iv) 100m + 1000n
(v) -p2q2 +7pq
(vi) 1.2 a + 0.86
(vii) 3.14r2
(viii) 2(l + b)
(ix) 0.1y + 0.01y2

Answer - 4 : -


Question - 5 : - (a) Identify terms which contain x and give the
coefficient of x.
(i) y2x + y
(ii) 13y2 – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12 xy2 + 25
(vii) 7x + xy2

Answer - 5 : -


Question - 6 : - (b) Identify terms which contain y2 and give the coefficients of y2.
(i) 8 – xy2
(ii) 5y2 + 7x
(iii) 2x2y – 15xy2 + 7y2

Answer - 6 : -

Question - 7 : - 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) 4p2q – 4pq2
(viii) 7mn
(ix) z2 – 3z + 8
(x) a2 + b2
(xi) z2 + z
(xii) 1 + x + x2

Answer - 7 : -

(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

Question - 8 : - State whether a given pair of terms is of like orunlike terms.
(i) 1, 100
(ii) -7x, 5x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m2p, 4mp2
(vi) 12xz, 12 x2y2

Answer - 8 : -

(i) 1,100 – Like
(ii) -7x, 5x– Like
(iii) -29x, -29y – Unlike
(iv) 14xy, 42yx – Like
(v) 4m2p, 4mp2 –Unlike
(vi) 12xz, 12x2z2 – Unlike

Question - 9 : - 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

Answer - 9 : -

(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, – 7qp, 78qp
(ii) 7p, 2405p
(iii) 8q, -100q
(iv) -p2q2,12 q2p2
(v) -23, 41
(vi) -5p2, 701p2
(vii) 13p2q, qp2

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