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Question
Factorise the following:
(p – q)2 – 6(p – q) – 16
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Solution
Let (p – q) = x
(p – q)2 – 6(p – q) – 16 = x2 – 6x – 16
Product = – 16, sum = – 6
Split the middle term as – 8x and 2x
x2 – 6x – 16 = x2 – 8x + 2x – 16
= x(x – 8) + 2(x – 8)
= (x – 8)(x + 2)
...(But x = p – q)
= (p – q – 8)(p – q + 2)
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