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Example 22: If m – n = 16 and m + n = 400, then find mn.
Quick Check
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Solutions: We know that, (m – n) = m – 2mn + n 2
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= m + n – 2mn ...(i) Using identities,
evaluate the following:
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Putting m – n = 16 and m + n = 400 in (i), we get 1. (103) 2. 105 × 95
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(16) = 400 – 2mn
⇒ 256 = 400 – 2mn
⇒ 2mn = 144
⇒ mn = 72
Practice Time 8E

1. Find the product of the following using suitable identity.
(a) (7t + 9u)(7t + 9u) (b) (2x – 5y)(2x – 5y) (c) (6a + 12b)(6a – 12b)

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(d) (x + y )(x – y ) (e)    1 x − 1 y 2   1 x − 1 y 2    (f)    8p + 6q  8p + 6q 
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 
 
5  
5 
 
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2. Find each square by using a suitable identity.
 6 7  2
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(a) (5x + 6) 2 (b)   7 x + 5   (c) (s t – tu ) (d) (0.9p – 0.5q) 2
y
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3. Use the identity (x + a)(x + b) = x + (a + b)x + ab to find the following products.
 2x 2a  2x 3a
(a) (x + 3)(x + 8) (b) (uvw – 4)(uvw – 5) (c) (9x + 10)(9x – 11) (d)   3 + 3   3 + 2  
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4. Use a suitable identity to evaluate each of the following.
(a) (51) 2 (b) (1005) 2 (c) 96 × 104 (d) 1.05 × 9.5
5. Find the value of ‘x’ if
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(a) 11x = (60) – (50) (b) pqx = (3p + q) – (3p – q) 2
6. Simplify the following.
(a) (8a – 9b) + (8a + 9b) (b) (3.5a – 2.5b) – (2.5a – 3.5b) 2
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(c) (xy + yz) – 2xy z (d) (x + 4)(x – 4)(x + 16)
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(e) (3x – 1)(3x + 1)(9x + 1)(81x + 1) (f) (a – b)(a + b) + (b – c)(b + c) + (c – a)(c + a)
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7. If x − = 5 , find the value of x + .
x x 2
8. Show that
 5 4  2 25 16
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t
(a) (5x + 8) – 160x = (5x – 8) 2 (b)   4 s − 5   + 2st = 16 s + 25 t 2
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9. Find the value of (9x + 12xy + 4y ) when x = and y = .
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Brain Sizzlers
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If (s + 3)(s + a) = s + 8s + b, then what will be the values of a and b?
209 Algebraic Expressions