Mathematics
Factorise the following:
1 - 2a - 2b - 3(a + b)2.
Factorisation
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Answer
1 - 2a - 2b - 3(a + b)2 = 1 - 2(a + b) - 3(a + b)2.
Let (a + b) = t.
1 - 2a - 2b - 3(a + b)2 = 1 - 2t - 3t2
Factorising we get,
1 - 2t - 3t2 = 1 - 3t + t - 3t2
= 1(1 - 3t) + t(1 - 3t)
= (1 + t)(1 - 3t)
= (1 + a + b)[1 - 3(a + b)]
= (1 + a + b)(1 - 3a - 3b).
Hence, 1 - 2a - 2b - 3(a + b)2 = (1 + a + b)(1 - 3a - 3b).
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