Page 109 - Start Up Mathematics_8 (Non CCE)

(b) (4x – 3)(4x + 5)
\ (4x – 3)(4x + 5) = (y – 3)(y + 5) (Putting 4x = y)
2
2
= y + (–3 + 5)y + (–3) ¥ 5 {Using (x + a)(x + b) = x + (a + b)x + ab}
2
= y + 2y – 15
2
= (4x) + 2(4x) – 15 (Putting y = 4x)
2
= 16x + 8x – 15
2
Example 34: Evaluate the following using (x + a)(x + b) = x + (a + b)x + ab:
(a) 104 ¥ 101 (b) 54 ¥ 47 (c) 96 ¥ 99
Solution: (a) 104 ¥ 101 = (100 + 4) ¥ (100 + 1) (Here x = 100, a = 4, b = 1)
2
= (100) + (4 + 1)100 + (4 ¥ 1)
= 10,000 + 500 + 4 = 10,504
(b) 54 ¥ 47 = (50 + 4) ¥ (50 – 3) (Here x = 50, a = 4, b = –3)
2
= (50) + {4 + (–3)}50 + 4 ¥ (–3)
= 2,500 + (1)(50) – 12 = 2,500 + 50 – 12 = 2,538
(c) 96 ¥ 99 = (100 – 4) ¥ (100 – 1) (Here x = 100, a = –4, b = –1)
2
= (100) + {(–4) + (–1)}100 + (–4) ¥ (–1)
= 10,000 + (–5)100 + 4 = 10,000 – 500 + 4 = 9,504

EXERCISE 5.7

1. Find the following products:
(a) (x + 2)(x + 6) (b) (x + 3)(x – 4) (c) (x – 7)(x – 5) (d) (4x + 7)(4x – 3)

Ê 3 ˆ Ê 3 ˆ Ê 2 ˆ Ê ˆ 5 2 2
(e) Á Ë 4 y - 2 ˜ Á 4 y + 4 (f) Á Ë x + 5 ˜ Á x + ˜ (g) (7x – 6xy)(7x – 3xy)
˜
¯
¯ Ë
¯ Ë
¯ 2
Ê 1ˆ Ê 3ˆ
2
(h) Á Ë l - 2¯ Ë l + 4¯ ˜
2
˜ Á
2
2. Evaluate the following using the identity (x + a)(x + b) = x + (a + b)x + ab.
(a) 103 ¥ 105 (b) 108 ¥ 106 (c) 97 ¥ 96 (d) 102 ¥ 95
(e) 59 ¥ 48 (f) 28 ¥ 33 (g) 995 ¥ 1,004 (h) 45 ¥ 47

MATHS LAB ACTIVITY

2
Objective: To show that (x + a)(x + b) = x + (a + b)x + ab
Material required: Sketch pen, scale, a rectangular piece of cardboard, a pair of scissors, glue stick/
fevicol, colours, sheet of paper
Method:
Step 1. On a piece of cardboard, draw a rectangle WING of length (x + a) cm and breadth (x + b) cm.
Mark a point P on WI so that WP = x and a point Q on IN so that IQ = x.

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