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Factoring using Difference of cubes

Q:  How do I factor this:  27 – 64x6

A:  This looks like a difference of cubes… How do I know?  It looks like (something cubed) – (something else cubed).

The difference of cubes formula is one you have to memorize or just have handy… It says:

a3 – b3 = (ab)(a2 + ab + b2)

[I color-coded it to make it easier for the next steps].

OK, back to our original problem…  I need to make it look like (something)3 – (something)3

27 – 64x6 = 3³ – (4x2

So, we have:

3³ – (4x2)³ = (34x2)(32 + 3*4x2 + (4x2)2)

Now, simplify the right side:

(3 – 4x2)(32 + 3*4x2 + (4x2)2) = (3 – 4x2)(9 + 12x2 + 16x4)

There it is!

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