Mathematics
Factorise the following:
3 - 5a - 5b - 12(a + b)2
Factorisation
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Answer
3 - 5a - 5b - 12(a + b)2 = 3 - 5(a + b) - 12(a + b)2.
Let (a + b) = t.
3 - 5(a + b) - 12(a + b)2 = 3 - 5t - 12t2
Factorising we get,
3 - 5t - 12t2 = 3 - 9t + 4t - 12t2
= 3(1 - 3t) + 4t(1 - 3t)
= (1 - 3t)(3 + 4t)
= [1 - 3(a + b)][3 + 4(a + b)]
= (1 - 3a - 3b)(3 + 4a + 4b).
Hence, 3 - 5a - 5b - 12(a + b)2 = (1 - 3a - 3b)(3 + 4a + 4b).
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