Question

can someone show me how to factor

6x^2 - 3xy - 3y^2

Answer 1

Why do you believe it CAN be factored?

Answer 2

because my book has the answer in the answer key

Answer 3

That's a pretty good reason, but hardly scriptural.

You can narrow it down. 3 is prime. Your answer MUST look like this:

(__ x + y)(__ x - 3y)

You just have to find the right factors of 6 to make it work.

1, 6
6, 1
2, 3
3, 2

There you have it. Only four things to try.

Answer 4

hmm the answer is 3(2x + y)(x - y)

Answer 5

Try 2, 3 from my list.

Answer 6

well that would make (2x + y) (3x - 3y) thats not the answer though?

Answer 7

Have you considered the Distributive Property? (3x-3y) = 3(x-y)

Answer 8

sorry i dont understand that would still make (2x + y) 3(x - y) no?

Answer 9

Have you considered the commutative property?

(2x+y)3(x-y) = 3(2x+y)(x-y)

These are important properties. You are expected to have them in your bag of tricks.

Also, I failed to notice that all the coefficients were divisible by 3. This would have made our lives easier.

6x^2 - 3xy - 3y^2 = 3(2x^2 - xy - y^2) =

One of these

3(2x + y)(x - y) or 3(2x - y)(x + y)