Page 93 - Start Up Mathematics_8 (Non CCE)

EXERCISE 5.2

1. Add the following algebraic expressions:
2
2
2
2 2
2
2 2
2 2
2
2 2
(a) 8a – 5ab + 3b , 2ab – 6b + 3a , b + ab – 6a 2 (b) 8p q , –5p q , 3p q , –p q
(c) 6px – 2qy + 3rz, 6qy – rz – 11px, 10rz – 2px – 3qy
13 14 15 13 14 15
(d) xy + y + x -, y - x - xy
2 5 7 2 5 7
2
2
2
2
2
(e) 4p – 7pq + 4q – 3, p – 8pq + 5 + 6q , 6 – 2pq – 5q + 2p 2
2 5 5 - 4 2x 2 x 5x 3 6
2
2
(f) 2, x - x + x 3 , + - , + 3x + 3x +
3 3 2 3 3 2 3 5
2. Subtract:
2
4
3
4
3
2
(a) 7x – 5x + 4x + 3x – 3 from 6x – 4x – 8x – 2x + 7
4 4 2 6 xy 35 6 2 4
3
3
2
2
3
(b) x - x - 5 from x + x + 2x - (c) - yz + xz from yz - xz
3 7 3 7 5 3 7 7 7
7 3 1 7 9 y y 2
3
2
(d) y + y + y + from - -
4 5 2 2 2 3 5
2
2
2
2
2
2
3. What must be subtracted from 3x – 4y – 5z – 6 to get 4x + 5y – 6z + 7?
4. Subtract –p + 6q – r from the sum of 3p – 4q + 4r and 2p + 3q – 8r.
5. Subtract the sum of –6b + c + a and –3a + 2c + 3b from the sum of 5a – 8b + 2c and 3c – 4b – 2a.
6. The two adjacent sides of a rectangular plot are y – 6x + 3z + 8 and x – 2y – 5z – 8. Find the perimeter
of the plot.
7. Simplify the following:
(a) (a – 3b + 2c) + (–4a + 9b – 11c) – (3a – 4b – 7c) (b) {7 – 2x + 3y – (3x – y)} – (2x – 5y + 11)
1 1 1 1 1 1 1
2
2
2 2
2
2
2
2
2
(c) zx y - z xy + zy x - zyx - xyz + xy z - x yz
8 7 6 5 4 3 2
Multiplication of Algebraic Expressions
(i) Rules of signs:
The product of two factors having same signs is positive i.e., (+) ¥ (+) = (+) and (–) ¥ (–) = (+).
The product of two factors having different signs is negative i.e., (+) ¥ (–) = (–) and (–) ¥ (+) = (–).
m
n
(ii) If x is any variable and m, n are positive integers, then x ¥ x = x m + n .
6
5
7 4
2
For example, x ¥ x = x 2 + 5 = x , y ¥ y = y 4 + 6 = y 10
The result of two algebraic expressions when multiplied is called product and the expressions are called
factors or multiplicants.
Multiplication of two monomials
The coefficient of the product of two monomials is the product of their coefficients and the variable in the
product of two monomials is equal to the product of the variables in the given monomials.
3
2
2
m
3
n
For example, (6x y) ¥ (4xy ) = (6 ¥ 4) ¥ (x ¥ x) ¥ (y ¥ y ) (x ¥ x = x m + n )
= 24 ¥ x 2+1 ¥ y 1 + 3
3
= 24 ¥ x ¥ y 4
3 4
= 24x y
2
3
3 4
\ (6x y) ¥ (4xy ) = 24x y
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