Mathematics
Factorise the following:
a(2a - b) - b2
Factorisation
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Answer
a(2a - b) - b2 = 2a2 - ab - b2.
To factorise 2a2 - ab - b2, we want to find two real numbers whose sum is -1 and product is 2 × (-1) = -2. By trial, we see that (-2) + 1 = -1 and (-2) × 1 = -2.
∴ 2a2 - ab - b2 = 2a2 - 2ab + ab - b2
= 2a(a - b) + b(a - b)
= (a - b)(2a + b).
Hence, a(2a - b) - b2 = (a - b)(2a + b).
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