Factor the polynomials completely 10x^6-4x^8 And... 64x^3-27y^3?



Factor the polynomials completely
10x^6-4x^8 And… 64x^3-27y^3 ?


First step is to identify the greatest common factor for each term which is 2x⁶. Then factor it out


This cannot be factored further and so it is the answer.


The first step is to recognize that each term is a perfect cube.

64x³ = (4x)³
27y³ = (3y)³

so, this is a difference of two cubes pattern. You have to have memorized the pattern, but it looks like this:

a³-b³ = (a-b)(a²+ab+b²)

In this case “a” is your first cube root of 4x, and “b” is the 2nd cube root of 3y

So writing out the pattern using this situation gives us

(4x)³-(3y)³ = (4x-3y)[(4x)²+(4x)(3y)+(3y)²]

simplifying that last factor gives us


which is the final answer.