**Q: How do I factor this: 27 – 64x ^{6}**

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:

a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})

[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 – 64x^{6} = 3³ – (4x^{2})³

So, we have:

3³ – (4x^{2})³ = (3 – 4x^{2})(3^{2} + 3*4x^{2} + (4x^{2})^{2})

Now, simplify the right side:

(3 – 4x^{2})(3^{2} + 3*4x^{2} + (4x^{2})^{2}) = (3 – 4x^{2})(9 + 12x^{2} + 16x^{4})

There it is!