Page 79 - Maths Skills - 8

Algebraic Expressions and Identities 77

2. Find the products of:
(i) (– 2xy )(5y)(– 3z ) (ii) (ab)(bc)(ca)
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2

5 9 7
(iii) (6a b)(– 2b c)(3ac ) (iv) ab bc ca
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2
2
9 7 5
1
3. Find the value of (3p q) × (8q ), when p = 1 and q = .
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2

4
1 2
4. Find the value of (– 8x y ) × xy , when x = – 1 and y = 2.
2 3
5
5. Find the product of (3a b ), (– 7a ) and (5a b ), and then verify the result for a = 2 and b = 3.
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2
2 3
6. Find the product of the following.
(i) 2x(3x + y ) (ii) (– 3y)(x + 3xy)
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2
(iii) 3a (4a – 5a ) (iv) – 8a b(– 3a – 2b)
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2
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(v) − 5 abc 18 abc − 3 abc 2   (vi) 7a(0.1a – 0.5b)
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2

9 15 10 
Multiplication of Two Binomials
In multiplication of two binomials, we use the distributive law twice to get the required product,
i.e., (a + b) × (c + d) = a × (c + d) + b × (c + d)
= (a × c) + (a × d) + (b × c) + (b × d) = ac + ad + bc + bd
For example, (2a + 3b) × (6a – b)
= 2a (6a – b) + 3b (6a – b) = (2a × 6a – 2a × b) + (3b × 6a – 3b × b)

= 12a – 2ab + 18ab – 3b = 12a + 16ab – 3b 2
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2
2
Multiplication of a Binomial and a Trinomial
To multiply a binomial by a trinomial, we simply apply distributive law as many times as required,
i.e., (a + b) × (p + q + r) = a (p + q + r) + b (p + q + r)

= ap + aq + ar + bp + bq + br
For example, (5x – 3) × (3x + 2y – 4) = 5x (3x + 2y – 4) – 3 (3x + 2y – 4)
= (5x × 3x) + (5x × 2y) – (5x × 4) – (3 × 3x) – (3 × 2y) – {3 × (– 4)}

= 15x + 10xy – 20x – 9x – 6y + 12 = 15x + 10xy – 29x – 6y + 12
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2

Let’s Attempt

Example 1: Multiply: (3x + 4y ) by (4x + 3y ).
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3
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Solution: (3x + 4y ) × (4x + 3y )
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3
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3
= 3x (4x + 3y ) + 4y (4x + 3y )
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3
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3
= (3x × 4x + 3x × 3y ) + (4y × 4x + 4y × 3y ) = (12x + 9x y ) + (16x y + 12y )
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3 3
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3
3 3
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= 12x + 25x y + 12y 6
3 3
6