Given the expression: 5x10 - 80x2 Part A: Rewrite the expression by factoring out the greatest common factor. Part B: Factor the entire expression completely. Show the steps of your work.

5x^2 (x^2 - 2) (x^2 + 2) (x^2+2x+2) (x^2-2x+2)

Step-by-step explanation:

5x^10 - 80x^2

The greatest common factor is 5x^2

5x^2 (x^8 - 16)

Rewriting the parentheses

5x^2 (x^4 ^2 - 4^2)

We notice the difference of squares (a^2 - b^2) = (a-b) (a+b)

5x^2 (x^4 - 4) (x^4+4)

Again rewriting the first parentheses

5x^2 (x^2 ^2 - 2^2) (x^4+4)

5x^2 (x^2 - 2) (x^2 + 2) (x^4+4)

The last term can be rewritten as (x^2+2x+2) (x^2-2x+2)

5x^2 (x^2 - 2) (x^2 + 2) (x^2+2x+2) (x^2-2x+2)