Question

Factories 2a3+16b3-5a-10b

Answer 1

Given Equation is 2a^3 + 16b^3 - 5a - 10b.

This can be written as 

2(a^3 + 8b^3) - 5a - 10b

We know that a^3 + b^3 = (a+b)(a^2-ab+b^2)

= > 2(a + 2b)(a^2 - 2ab + 4b^2) - 5a - 10b

= > 2(a + 2b)(a^2 - 2ab + 4b^2) - 5(a + 2b)

= > (a + 2b)(2(a^2 -2ab + 4b^2) - 5)

= > (a + 2b)(2a^2 - 4ab + 8b^2 - 5)

Therefore the equation can be factorized as (a + 2b)(2a^2 - 4ab + 8b^2 - 5).