Page 83 - Maths Skills - 8

Algebraic Expressions and Identities 81

Example 6: Using the identities, evaluate the following.

(i) 1.73 × 0.27 (ii) 5.4 × 4.6
Solution: (i) 1.73 × 0.27 = (1 + 0.73) (1 – 0.73) (ii) 5.4 × 4.6 = (5 + 0.4)(5 – 0.4)
2
= (1) – (0.73) 2 = (5) – (0.4) 2
2
= 1 – 0.5329 = 0.4671 = 25 – 0.16 = 24.84

Exercise 5.4

1. Find the following products.

(i) (5x + 9)(5x – 9) (ii) (x + y )(x – y ) (iii) x 1 x 1
2
3
3
2

2. Find the following products. x x
(i) (5x – 3y)(5x – 3y) (ii) (y – 3)(y – 3) (iii) 3 x 5 3 x 5
y
y

3. Find the following products. 4 6 4 6
(i) (x + 3)(x + 3) (ii) (2a + 3b)(2a + 3b) (iii) 2 x 5 2 x 5

3 3
4. Simplify using identities.
(i) 133 × 133 – 121 × 121 (ii) 5.89 × 5.89 – 0.11 × 0.11
(iii) 93 93 55 (iv) 3293 29 0170 17. . . .
88 312
.
1 1
2
5. If x = 3, find the value of x 2 .

x x
6. Using the identities, evaluate the following.
(i) 102 (ii) 311 (iii) 72 (iv) 89 (v) 118 (vi) 989 2
2
2
2
2
2
(vii) 13 × 7 (viii) 73 × 67 (ix) 9.3 × 8.7 (x) 12.5 × 11.5 (xi) 105 × 95 (xii) 153 × 147
ASSESSMENT TIME

3. If 3x – 2y = 8 and xy = 5, then the value of
COMPETENCY BASED QUESTIONS
9x + 4y will be:
2
2
A. Multiple-Choice Questions (i) 4 (ii) 69 (iii) 59 (iv) 124
1. The equivalent of a – 2ab + b is:
2
2
(i) (a + b) (ii) (a – b) 2 4. If x + 1 = 4, then the value of x + x 1 2 will be:
2
2
x
(iii) a – b (iv) none of these (i) 14 (ii) 18 (iii) 17 (iv) 15
2
2
2. When x = 2 and y = 3, then the value of 5. The value of 4x + 2x + 1 when x = – 2 is
2
2x – 3xy + 5y is equal to: equal to:
2
2
(i) 35 (ii) 53 (iii) 41 (iv) 14 (i) 15 (ii) 20 (iii) 18 (iv) 13