How do I factor the following: 27c^3 -64

Question

How do I factor the following:  27c^3 -64

mertsj · Answer

Use the difference of cubes formula which is:

mertsj · Answer

$$a^3-b^3=(a-b)(a^2+ab+b^2)$$

anonymous · Answer

Mind if I help our Mertsj?

anonymous · Answer

*out

mertsj · Answer

As long as you don't just write down the answer.

anonymous · Answer

Well, it'll be kind of difficult to not just write down the answer since it's so simple, so I guess I'll just let you handle it :).

homeworksucks · Answer

so cube root the first number, that gives you your a value, cube rooting the second gives you your b-value, and just plug those in

homeworksucks · Answer

remember subtracting a negative is adding a positive

anonymous · Answer

so would 'a' end up equaling '3c?'

mertsj · Answer

yes

anonymous · Answer

I did the formulae, and it became a binomial multiplied by a trinomial, but when I simplified that I did not get a answers that I think is correct

mertsj · Answer

$$27c^3-64=(3c-4)(9c^2+12c+16)$$

anonymous · Answer

wouldn't that be a negative 12c?

mertsj · Answer

Did you see my previous post:  a^3−b^3=(a−b)(a^2+ab+b^2)

anonymous · Answer

o yes I get it now

mertsj · Answer

Good for you.

anonymous · Answer

so is that fully simplified?

anonymous · Answer

o wait it is not

mertsj · Answer

yes it is fully simplified.

anonymous · Answer

so the fully simplified answer would be (3c-4)(3c+12)(3c-8)?

mertsj · Answer

That would be correct IF (3c+12)(3c-8)=9c^2+12c+16
Does it?

anonymous · Answer

yes

mertsj · Answer

What are you smokin' ?

anonymous · Answer

oooo... it does not.

mertsj · Answer

The factors of 27c^3-64 are (3c-4)(9c^2+12c+16)
Now could we please put this problem to bed?