Page 104 - Start Up Mathematics_7

Example 14: If p = –2, find the value of:
2
3
(a) 4p + 8 (b) –2p – 3p + 4p + 7
Solution: (a) Value of (4p + 8), when p = –2 is 4(–2) + 8 = –8 + 8 = 0.
2
2
3
3
(b) Value of (–2p – 3p + 4p + 7) when p = –2 is –2(–2) – 3(–2) + 4(–2) + 7
= 16 – 12 – 8 + 7 = 3.
Example 15: Find the value of the following expressions, when x = –1:
2
(a) 2x + 7 (b) 3 – 2x (c) x + 2x + 1
Solution: (a) Value of (2x + 7), when x = –1 is 2(–1) + 7 = 5.
(b) Value of (3 – 2x), when x = –1 is 3 – 2(–1) = 3 + 2 = 5.
2
2
(c) Value of x + 2x + 1, when x = –1 is (–1) + 2(–1) + 1 = 1 – 2 + 1 = 0.
Example 16: If a = 1, b = –1, find the value of:
2
2
2
(a) a + b 2 (b) a + ab + b 2 (c) a – b 2
2
2
2
2
Solution: (a) Value of a + b , when a = 1, b = –1 is (1) + (–1) = 1 + 1 = 2.
2
2
(b) Value of a + ab + b , when a = 1, b = –1 is
2
2
(1) + (1)(–1) + (–1) = 1 – 1 + 1 = 1.
2
2
2
2
(c) Value of a – b , when a = 1, b = –1 is (1) – (–1) = 1 – 1 = 0.
Example 17: When a = 0, b = –1, find the value of the given expressions:
2
(a) 3a + 2b (b) a(b + b + 1) (c) (a + b)(a + 1)(b + 1)
Solution: (a) Value of 3a + 2b, when a = 0, b = –1 is 3(0) + 2(–1) = –2
2
(b) Value of a(b + b + 1) when a = 0, b = –1 is 0
(c) Value of (a + b)(a + 1)(b + 1) when a = 0, b = –1 is (0 – 1)(0 + 1)(–1 + 1)
= (–1)(1)(0) = 0
Example 18: Simplify the following expressions and find the value when x = 2.
(a) 2(5 – 2x) + 3(1 – 4x) (b) 3(2x + 1) + 5x – 2
Solution: (a) 2(5 – 2x) + 3(1 – 4x) = 10 – 4x + 3 – 12x
= (10 + 3) – (4x + 12x) = 13 – 16x
Value of (13 – 16x) when x = 2 is 13 – 16 × 2 = 13 – 32 = –19.
(b) 3(2x + 1) + 5x – 2 = 6x + 3 + 5x – 2
= (6x + 5x) + (3 – 2) = 11x + 1
Value of (11x + 1) when x = 2 is 11 × 2 + 1 = 22 + 1 = 23

Example 19: Simplify these expressions and find their values if x = 3, a = –1, b = –2.
(a) 2a + 4 + 3a + 1 (b) 9 – 8x + 4x + 4 (c) a – b + abx + 2b
Solution: (a) 2a + 4 + 3a + 1 = (2a + 3a) + (4 + 1) = 5a + 5
Value of (5a + 5) when a = –1 is 5(–1) + 5 = 0
(b) 9 – 8x + 4x + 4 = (9 + 4) + (–8x + 4x) = 13 – 4x
Value of 13 – 4x, when x = 3 is 13 – 4 × 3 = 13 – 12 = 1

(c) a – b + abx + 2b = a + b + abx
Value of (a + b + abx) when a = –1, b = –2 and x = 3 is
(–1) + (–2) + (–1)(–2)(3) = –1 – 2 + 6 = 3

96