How do you factor $(x^2+8)^2-36x^2$ ?

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Answer 1 · 2015-11-05T16:25:48

$(x^2+6x +8)(x^2-6x+8)$

As you can see, you have the difference of two squares: $(x^2+8)^2$ is obviously the square of $(x^2+8)$ , and $36x^2$ is the square of $6x$ .

A known formula states that the difference of squares is

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

So, we have that

$(x^2+8)^2-36x^2 = (x^2+8 +6x)(x^2+8-6x)$

How do you factor (x^2+8)^2-36x^2(x^2+8)^2-36x^2?