Question

Given the expression: 3x^10 − 48x^2 Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

Answer:

A) $3x^2(x^8-16)$

B)  $3x^2(x^4+4)(x^2+2)(x^2-2)$

Step-by-step explanation:

Part A:

=> $3x^{10} - 48x^2$

The greatest common factor is $3x^2$, So we'll take  $3x^2$ as common

=> $3x^2(x^8-16)$

Part B:

=> $3x^2(x^8-16)$

=> $3x^2[(x^4)^2-(4)^2]$

Using Formula $a^2-b^2 = (a+b)(a-b)$

=> $3x^2 (x^4+4)(x^4-4)$

=> $3x^2(x^4+4)[(x^2]^2-(2)^2]$

Again Using the same formula

=> $3x^2(x^4+4)(x^2+2)(x^2-2)$