Mathematics
Factorise the following:
250(a - b)3 + 2
Factorisation
33 Likes
Answer
250(a - b)3 + 2 = 2[125(a - b)3 + 1]
= 2[{5(a - b)}3 + 13]
We know that,
a3 + b3 = (a + b)(a2 - ab + b2).
∴ 2[{5(a - b)}3 + 13] = 2[(5a - 5b + 1){(5a - 5b)2 - (5a - 5b)1 + 12}]
= 2(5a - 5b + 1)(25a2 + 25b2 - 50ab - 5a + 5b + 1).
Hence, 250(a - b)3 + 2 = 2(5a - 5b + 1)(25a2 + 25b2 - 50ab - 5a + 5b + 1).
Answered By
25 Likes