## Chapter 9 Algebraic Expressions and Identities Exercise 9.1

Question 1: Identify the terms, their coefficients for each of the following expressions.
i) 5xyz² - 3zy
ii) 1 + x + x²
iii) 4x²y² - 4x²y²z² + z²
iv) 3 - pq + qr - rp
v) x/2 + y/2 - xy
vi) 0.3a - 0.6ab + 0.5b

Question 2: Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?
x + y, 1000, x + x² + x³ + x⁴, 7 + y + 5x, 2y - 3y², 2y - 3y² + 4y³, 5x - 4y + 3xy, 4z - 15z², ab + bc + cd + da, pqr, p²q + pq², 2p + 2q

i) ab - bc, bc - ca, ca - ab
ii) a - b + ab, b - c + bc, c - a + ac
iii) 2p²q² - 3pq + 4, 5 + 7pq - 3p²q²
iv) l² + m², m² + n², n² + l², 2lm + 2mn + 2nl

i)
= (ab - bc) + (bc - ca) + (ca - ab)
= ab - bc + bc - ca + ca - ab
= ab - ab - bc + bc - ca + ca
= 0 - 0 - 0
= 0

ii)
= (a - b + ab) + (b - c + bc) + (c - a + ac)
= a - b + ab + b - c + bc + c - a + ac
= a - a - b + b + ab - c + c + bc + ac
= 0 - 0 + ab - 0 + bc + ac
= ab + bc + ac

iii)
= (2p²q² - 3pq + 4) + (5 + 7pq - 3p²q²)
= 2p²q² - 3pq + 4 + 5 + 7pq - 3p²q²
= 2p²q² - 3p²q² - 3pq + 7 pq + 4 + 5
= -p²q² + 4pq + 9

iv)
= (l² + m²) + (m² + n²) + (n² + l²) + (2lm + 2mn + 2nl)
= l² + m² + m² + n² + n² + l² + 2lm + 2mn + 2nl
= l² + l² + m² + m² + n² + n² + 2lm + 2mn + 2nl
= 2l² + 2m² + 2n² + 2lm + 2mn + 2nl
= 2(l² + m² + n² + lm + mn + nl)

Question 4:
a) Subtract 4a - 7ab + 3b + 12 from 12a - 9ab + 5b - 3.
b) Subtract 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10xyz
c) Subtract 4p²q - 3pq + 5pq² - 8p + 7q - 10 from 18 - 3p - 11q + 5pq - 2pq² + 5p²q

a)
= (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)
= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12
= 12a - 4a - 9ab + 7ab + 5b - 3b - 3 - 12
= 8a - 2ab + 2b - 15

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

c)
= (18 - 3p - 11q + 5pq - 2pq² + 5p²q) - (4p²q - 3pq + 5pq² - 8p + 7q - 10)
= 18 - 3p - 11q + 5pq - 2pq² + 5p²q - 4p²q + 3pq - 5pq² + 8p - 7q + 10
= 18 + 10 - 3p + 8p - 11q - 7q + 5pq + 3pq - 2pq² - 5pq² + 5p²q - 4p²q
= 28 + 5p - 18q + 8pq - 7pq² + p²q