Mathematics
Factorise the following:
(4 - x)2 - 2x
Factorisation
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Answer
We know that,
(a - b)2 = a2 + b2 - 2ab.
∴ (4 - x)2 - 2x = 16 + x2 - 8x - 2x = 16 + x2 - 10x.
Rearranging the above terms we get,
x2 - 10x + 16.
To factorise x2 - 10x + 16, we want to find two real numbers whose sum is -10 and product is 16. By trial, we see that (-8) + (-2) = -10 and (-8) × (-2) = 16.
∴ x2 - 10x + 16 = x2 + (-8x) + (-2x) + 16
= x2 - 8x - 2x + 16
= x(x - 8) - 2(x - 8)
= (x - 8)(x - 2).
Hence, (4 - x)2 - 2x = (x - 8)(x - 2).
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