Question

Factor out the greatest common factor of Given the expression: 4x^10 − 64x^2

​

Answer 1

Below.

Explanation:

The GCF = 4x^2

So its 4x^2(x^8 - 16)

This can be further factored

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

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

Answer 2

Part A

4x10 – 64x2

= 4x2 * x8 – 4x2 * 16

= 4x2 * (x8 – 16) by distributive property

Part B

x8 is (x4)2 and 16 = 42 so a difference of squares is seen in the parentheses. The pattern a2 – b2 = (a + b)(a – b) can be used.

4x2 * (x8 – 16)

= 4x2 * (x4 + 4) * (x4 – 4)

x4 = (x2)2 and 4 = 22 so there is another difference of squares in the last factor. Use the pattern again.

= 4x2 * (x4 + 4) * (x2 + 2) * (x2 – 2)