Page 145 - ICSE Math 7

EXERCISE 12.3

1. Multiply.
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(a) 9a by 3 (b) –4x by 3 (c) 30ab by –3a (d) –4lm by –lm
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(e) 8x by 4x (f) 2a by 14xy (g) 5ab by 5a b
2. Simplify the following.
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(a) 3x × (2x + 5xy) (b) (–4a b) × (5ab + 3a – b )
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(c) 2a × (–5x) × 4a b (d) 4p q × 2pq × (–10p )
(e) (7x – 6y) × (6x – 7y) (f) (xy + yz + xz) × (x + y + z)
3. Evaluate the following.
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(a) (a + b) (a – b) (b) (a + b) (a – b) (a – b ) (c) (a + b) (a – b) (a – b ) (a + b )
4. Divide.
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(a) 3ab by –4ab (b) –125x y by –25x
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(c) 40p q by 8pq (d) 20x y z by –4x z
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(e) –27p q r + 9pq by –3pqr (f) 6a b + 12ab – 24a b by 6a b
5. Divide and verify the answer.
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(a) 8x – 6y – 8xy by 2x – 3y (b) 18a – 50a + 25a by 6a – 5
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(c) 9l + 18l – 9 by 3l + 3 (d) 4p – 3p + 6 by 4p – 3
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6. The area of a rectangle is (5l + 2lb – 3b ) sq. unit. If its length is (5l – 3b) units, find its breadth.
Also, find the perimeter of the rectangle.
Value of an Algebraic Expression
The value of an expression can be found by substituting the given value of literal in the expression.
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For example, value of x + 2x + 1 when x = 5 is 5 + 2 × 5 + 1 = 25 + 10 + 1 = 36.
Example 13: If m = 2, find the value of:
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(a) 3m – 2m + 7 (b) 9m – 5
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Solution: (a) Value of (3m – 2m + 7) when m = 2 is 3(2) – 2(2) + 7 = 12 – 4 + 7 = 15.
(b) Value of 9m – 5 when m = 2 is 9(2) – 5 = 9 – 5 = 4.
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Example 14: 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.
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