Question

64a^3 b^3-125c^3

Which algebraic identity is used in this?

Answer with steps

Answer 1

`64a^3b^3-125c^3=(4ab-5c)(16a^2b^2+40abc+25c^2)`

Explanation:

You have the following polynomial:

`64a^3b^3-125c^3`

This expression is of the form:

`x^3-y^3`

that is, a difference between cubes. The factorization of such a polynomial is given by:

`x^3-y^3=(x-y)(x^2+2xy+y^2)`

You apply the last expression to the polynomial given in the problem. But first you have:

`x^3=64a^3b^3\\\\y^3=125c^3\\\\x=4ab\\\\y=5c`

finally, you obtain:

`64a^3b^3-125c^3=(4ab-5c)((4ab)^2+2(4ab)(5c)+(5c)^2)\\\\64a^3b^3-125c^3=(4ab-5c)(16a^2b^2+40abc+25c^2)`