Exercise 8.4
1. Multiply the binomials.
(i) (2x + 5) and (4x – 3)
(2x + 5)(4x – 3) = 2x x 4x – 2x x 3 + 5 x 4x – 5 x 3 =
(ii) (y – 8) and (3y – 4)
( y – 8)(3y – 4) = y x 3 y +
= 3 y 2 − 4 y − 24 y + 32 = 3 y 2
(iii) (2.5l – 0.5m) and (2.5l + 0.5m)
(2.5l – 0.5m)(2.5l + 0.5m) = 2.5l x 2.5l + 2.5l x 0.5m – 0.5m x 2.5l – 0.5m x 0.5m = l 2 m 2
= m 2
(iv) (a + 3b) and (x + 5)
(a + 3b)(x + 5) =
(v) 2 pq + 3 q 2 3 pq − 2 q 2
= p 2 q 2 pq 3 pq 3 q 4 p 2 q 2 pq 3 q 4
(vi) 3 4 a 2 + 3 b 2 4 a 2 − 2 3 b 2
= 3 4 a 2 x 4 a 2 − 8 3 b 2 + 3 b 2 x 4 a 2 − 8 3 b 2 3 4 a 2 x 4 a 2 − 3 4 a 2 x 8 3 b 2 + 3 b 2 x 4 a 2 − 3 b 2 x 8 3 b 2
= a 4 a 2 b 2 a 2 b 2 b 4 a 4 a 2 b 2 b 4
2. Find the product.
(i) (5 – 2x) (3 + x) = 5(3 + x) – 2x(3 + x) = x 2 x 2
(ii) (x + 7y) (7x – y) = x(7x-y) + 7y(7x-y) = x 2 y 2 x 2 y 2 xy
(iii) a 2 + b a + b 2 a 2 a + b 2 + b a + b 2 b 3
(iv) p 2 − q 2 2 p + q p 2 2 p + q − q 2 2 p + q p 3 p 2 q – pq 2 q 3 pq 2
3. Simplify.
(i) x 2 − 5 x + 5 + 25 = x 2 x 2 5 x
(ii) a 2 + 5 b 3 + 3 + 5 = a 2 b 3 b 3 a 2
(iii) t + s 2 t 2 − s t t 2 − s + s 2 t 2 − s t 3 s 2 t 2 s 3
(iv) (a + b)(c – d) + (a – b)(c + d) + 2(ac + bd) = (ac – ad + bc – bd) + (ac + ad – bc – bd) + (2ac + 2bd)
= ac – ad + bc – bd + ac + ad – bc – bd + 2ac + 2bd =
(v) (x + y)(2x + y) + (x + 2y)(x – y) = x 2 y 2 x 2 y 2 x 2 y 2
(vi) x + y x 2 − xy + y 2 x 2 y + xy 2 x 2 y – xy 2 y 3
(vii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y = x 2 y 2
=
(viii) (a + b + c)(a + b – c) = b 2 c 2
=