30 POINTS Given the expression: 6x10 − 96x2 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.

6x^2 ( x^2 -2) ( x^2 +2)(x^2+2x+2)(x^2-2x+2)

Step-by-step explanation:

6x^10 − 96x^2

Factor out 6x^2

6x^2 ( x^8 - 16)

Notice that inside the parentheses we have the difference of squares

6x^2 ( x^4 ^2 - 4^2)  a^2 - b^2 = (a-b) (a+b)

6x^2 ( x^4 -4) (x^4 +4)

Notice that x^4-4 is also the difference of squares

6x^2 ( x^2^2 -2^2) (x^4 +4)

6x^2 ( x^2 -2) ( x^2 +2) (x^4 +4)

Note also that x^4 + 4 can be factored into (x^2+2x+2)(x^2-2x+2)

6x^2 ( x^2 -2) ( x^2 +2)(x^2+2x+2)(x^2-2x+2)