Mathematics
Factorise the following:
2a3 + 16b3 - 5a - 10b
Factorisation
28 Likes
Answer
2a3 + 16b3 - 5a - 10b = 2(a3 + 8b3) - 5(a + 2b)
= 2[a3 + (2b)3] - 5(a + 2b)
We know that,
a3 + b3 = (a + b)(a2 - ab + b2).
∴ 2[a3 + (2b)3] - 5(a + 2b) = 2(a + 2b)(a2 - 2ab + 4b2) - 5(a + 2b)
= (a + 2b)[2(a2 - 2ab + 4b2) - 5]
= (a + 2b)(2a2 - 4ab + 8b2 - 5).
Hence, 2a3 + 16b3 - 5a - 10b = (a + 2b)(2a2 - 4ab + 8b2 - 5).
Answered By
17 Likes