Class 8 Maths

# Algebraic Expressions

## Exercise 9.1

Question 1: Identify the terms, their coefficients for each of the following expressions.

(i) 5xyz^2 – 3zy

Answer: Term: xyz^2 -- Coefficient = 5
Term: zy -- Coefficient = 3

(ii) 1 + x + x^2

Answer: Term: x -- Coefficient = 1 and Term: x^2 -- Coefficient = 1

(iii) 4x^2y^2 – 4x^2y^2z^2+ z^2

Answer: 4 is the coefficient for x^2y^2z^2
1 is the term for z^2

(iv) 3 – pq + qr – rp

Answer: For each term the coefficient is 1

(v) x/2-y/2=xy

Answer: 1/2 is the coefficient for x and y and for xy it is 1

(vi) 0.3a – 0.6ab + 0.5b

Answer: 0.3 is the coefficient for a, for b there are two coefficients 0.6 and 0.5

Question 2: Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

1. x + y: Binomial
2. 1000: Monomial
3. x + x^2 + x^3 + x^4: Polynomial
4. 7 + y + 5x: Binomial
5. 2y – 3y^2: Binomial
6. 2y – 3y^2 + 4y^3: Trinomial
7. 5x – 4y + 3xy: Trinomial
8. 4z – 15z^2: Binomial
9. ab + bc + cd + da: Polynomial
10. pqr: Mononomial
11. p^2q + pq^2: Binomial
12. 2p + 2q: Binomial

(i) ab – bc, bc – ca, ca – ab

Answer: (ab - bc) + (bc - ca) + (ca-ab)
=ab + bc + ca - bc - ca - ab= 0

(ii) a – b + ab, b – c + bc, c – a + ac

Answer: =(a - b + ab) + (b - c + bc) + (c - a + ac)
= a + b + c + ab + bc + ca - b - c - a
= ab + bc + ca

(iii) 2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2

Answer: = (2p^2q^2 - 3pq + 4) + (5 + 7pq - 3p^2q^2)
= 2p^2q^2 - 3p^2q^2 - 3pq + 7pq + 4 + 5
= - p^2q^2 + 4pq + 9

(iv) l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl

Answer: =(l^2 + m^2) + (m^2 + n^2) + (n^2 + l^2) + (2lm + 2mn + 2nl)
= l^2 + l^2 + m^2 + m^2 + n^2 + n^2 + 2lm + 2mn + 2nl
= 2l^2 + 2m^2 + 2n^2 + 2lm + 2mn + 2nl

Question 4: (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

Answer: (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)
= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12
(signs are reversed after –sign once bracket is opened)
= 8a - 2ab + 2b - 15

Question 4: (b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Answer: (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)
= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx
= 2xy - 7yz + 5zx + 10xyz

Question 4: (c) Subtract 4p^2q – 3pq + 5pq^2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq^2 + 5p^2q

Answer: (18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q) - (4p^2q - 3pq + 5pq^2 - 8p + 7q - 10)
= 18 - 3p - 11q + 5pq - 2pq^2 + 5p^2q - 4p^2q + 3pq - 5pq^2 + 8p - 7q + 10
= 28 + 5p - 18q + 8pq - 7pq^2 - p^2q