Question

GCF ( factoring completely). 2a^2 - 2b^2

Answer 1

\[2a^2-2b^2 = 2(a^2-b^2) = ?\]
How do you think the difference inside the parentheses could be factored?

Answer 2

2ab(a-b)????

Answer 3

2(a-a) (b-b)????

Answer 4

No, the last one would be equal to zero..

Answer 5

So whats the answer!?

Answer 6

Do you want the answer, or do you want to try to work it out step by step?

Answer 7

Step by step

Answer 8

Ok, let's play a game. If I told you that:
\[a^2-b^2 \]
can be written as a product of two parentheseses, the 1st of which is:
\[(a+b)\]
what do you think the other one would be?

Answer 9

(A-b)

Answer 10

Right! Bravo! So what would be the answer to you question?

Answer 11

2(a-b)(a+b)

Answer 12

Right! Well done!

Answer 13

If its 6x^2-6^2 would it be. The same??

Answer 14

6(x+y)(x-y)???? Or no

Answer 15

You could say that:
\[6x^2 - 6^2 = 6(x^2-6) = 6(x^2-\sqrt{6}^2)\]
Then you can do the same thing we did before.

Answer 16

But it's the gcf so can I say 3(x+y) 2(x-y)??

Answer 17

??????

Answer 18

I think it would be 6 in this case, but I'm not really sure