Question

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

Answer 1

Use the difference of cubes formula which is:

Answer 2

\[a^3-b^3=(a-b)(a^2+ab+b^2)\]

Answer 3

Mind if I help our Mertsj?

Answer 4

*out

Answer 5

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

Answer 6

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 :).

Answer 7

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

Answer 8

remember subtracting a negative is adding a positive

Answer 9

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

Answer 10

yes

Answer 11

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

Answer 12

\[27c^3-64=(3c-4)(9c^2+12c+16)\]

Answer 13

wouldn't that be a negative 12c?

Answer 14

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

Answer 15

o yes I get it now

Answer 16

Good for you.

Answer 17

so is that fully simplified?

Answer 18

o wait it is not

Answer 19

yes it is fully simplified.

Answer 20

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

Answer 21

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

Answer 22

yes

Answer 23

What are you smokin' ?

Answer 24

oooo... it does not.

Answer 25

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