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## 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.
y - z

(ii) One-half of the sum of numbers x and y.
1/2 (x + y) = x + y/2

(iii) The number z multiplied by itself.
z x z = z²

(iv) One-fourth of the product of numbers p and q.
1/4 (p x q) = pq/4

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

(vi) Number 5 added to three times the product of numbers m and n.
3mn + 5

(vii) Product of numbers y and z subtracted from 10.
10 - (y x z) = 10 - yz

(viii) Sum of numbers a and b subtracted from their product.
(a × b) - (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

Expression: x - 3
Terms: x, -3
Factors: x, -3

(b) 1 + x + x²
Expression: 1 + x + x²
Terms: 1, x, x²
Factors: 1; x; x, x

(c) y – y³

Expression: y – y³
Terms: y, -y³
Factors: y; -y, -y, -y

(d) 5xy² + 7x²y

Expression: 5xy² + 7x²y
Terms: 5xy², 7x²y
Factors: 5, x, y, y; 7, x, x, y

(e) -ab + 2b² – 3a²
Expression: -ab + 2b² – 3a²
Terms: -ab, 2b², -3a²
Factors: -a, b; 2, b, b; -3, a, a

(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5
(b) – 4x + 5y
(c) 5y + 3y²
(d) xy + 2x²y²
(e) pq + q
(f) 1.2 ab – 2.4 b + 3.6 a
(g) 3/4 x + 1/4
(h) 0.1 p2 + 0.2 q2

 Expression Terms Factors (a) - 4x + 5 -4x 5 -4, x 5 (b) - 4x + 5y -4x 5y -4, x 5, y (c) 5y + 3y² 5y 3y² 5, y 3, y, y (d) xy + 2x²y² xy 2x²y² x, y 2, x, x, y, y (e) pq + q pq q p, q q (f) 1.2 ab - 2.4 b + 3.6 a 1.2ab -2.4b 3.6a 1.2, a, b -2.4, b 3.6, a (g) 3/4 x + 1/4 3/4 x ¼ 3/4, x 1/4 (h) 0.1 p2 + 0.2 q2 0.1p² 0.2q² 0.1, p, p 0.2, q, q

Question 3: Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t²
(ii) 1 + t + t² + t³
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) – p²q² + 7pq
(vi) 1.2 a + 0.8 b
(vii) 3.14 r²
(viii) 2 (l + b)
(ix) 0.1 y + 0.01 y²

 Expression Terms Coefficients (i) 5 – 3t2 - 3t² -3 (ii) 1 + t + t2 + t3 t t² t³ 1 1 1 (iii) x + 2xy + 3y x 2xy 3y 1 2 3 (iv) 100m + 1000n 100m 1000n 100 1000 (v) – p2q2 + 7pq -p²q² 7pq -1 7 (vi) 1.2 a + 0.8 b 1.2a 0.8b 1.2 0.8 (vii) 3.14 r2 3.14r² 3.14 (viii) 2 (l + b) 2l 2b 2 2 (ix) 0.1 y + 0.01 y2 0.1y 0.01y² 0.1 0.01

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) 12xy² + 25
(vii) 7x + xy²

 Expression Terms Coefficient of x (i) y2x + y y2x y2 (ii) 13y2 – 8yx - 8yx -8y (iii) x + y + 2 x 1 (iv) 5 + z + zx x zx 1 z (v) 1 + x + xy xy y (vi) 12xy2 + 25 12xy² 12y² (vii) 7x + xy2 7x xy² 7 y²

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

 Expression Terms Coefficient of y2 (i) 8 - xy2 - xy2 - x (ii) 5y2 + 7x 5y2 5 (iii) 2x2y - 15xy2 + 7y2 - 15xy² 7y² - 15x 7

Question 5: Classify into monomials, binomials and trinomials.
(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
(Like term)
(ii) –7x, (5/2)x (Like term)
(iii) – 29x, – 29y (Unlike terms)
(iv) 14xy, 42yx (Like term)
(v) 4m2p, 4mp2 (Unlike terms)
(vi) 12xz, 12x²z² (Unlike terms)

Question 7: Identify like terms in the following:
(a) – xy², – 4yx², 8x², 2xy², 7y, – 11x², – 100x, – 11yx, 20x²y, – 6x², y, 2xy, 3x
– xy², 2xy²
– 4yx², 20x²y
8x², – 11x², – 6x²
7y, y
– 100x, 3x
– 11yx, 2xy

(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp,