Question

difference of squares
$a^2 - b^2$
example(s):

• $x^2 - 64$
• $18m^2n - 2n^3$

Explanation:

Step1: Factor $x^2-64$ as difference of squares

$x^2 - 64 = x^2 - 8^2 = (x+8)(x-8)$

Step2: Factor out GCF from $18m^2n-2n^3$

$18m^2n - 2n^3 = 2n(9m^2 - n^2)$

Step3: Factor remaining difference of squares

$9m^2 - n^2 = (3m)^2 - n^2 = (3m+n)(3m-n)$

Step4: Combine factors for the second example

$2n(3m+n)(3m-n)$

Answer:

1. $x^2 - 64 = (x+8)(x-8)$
2. $18m^2n - 2n^3 = 2n(3m+n)(3m-n)$