Chapter 12 Algebraic Expressions Exercise 12.1

Chapter 12 Algebraic Expressions Exercise 12.1

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

(ii) One half of the sum of numbers x and y

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

(iv) One-fourth of the product of numbers p and q

(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.
(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) y – y³
(d) 5xy² + 7x²y
(e) -ab + 2b² – 3a²
Solution:

(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

(h) 0.1p² + 0.2q²
Solution:

Question 3.
Identify the numerical coefficients of terms (other than 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
Solution:

Question 4.
(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
Solution:

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

Question 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) 4p²q – 4pq²
(viii) 7mn
(ix) z² – 3z + 8
(x) a² + b²
(xi) z² + z
(xii) 1 + x + x²
Solution:
(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 6.
State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) -7x, x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m²p, 4mp²
(vi) 12xz, 12 x²y²
Solution:
(i) 1, 100 – Like
(ii) -7x, x – Like
(iii) -29x, -29y – Unlike
(iv) 14xy, 42yx – Like
(v) 4m²p, 4mp² – Unlike
(vi) 12xz, 12x²z² – Unlike

Question 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
Solution:
(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