Question

how do you factor 4asquared-4ab+bsquared-csquared? PLEASE HELP!!!!!!!

Answer 1

4a^2-4ab+b^2-c^2
=(2a-b)^2-c^2

Answer 2

how did you do that?

Answer 3

remember the difference of squares formula.

Answer 4

xsquared-ysquared=(x+y)(x-y)??

Answer 5

yes.

Answer 6

(2a-b)^2-c^2
=(2a-b+c)(2a-b-c)

Answer 7

how does that apply?? theres more than 2 squared terms.

Answer 8

well, it does. I could show it to you by multiplying out, but let's do it an easier way.

Answer 9

ok

Answer 10

(2a-b)^2-c^2
->replace 2a-b with u.
u^2-c^2=(u+c)(u-c)
Replace u with 2a-b
(2a-b+c)(2a-b-c)

Answer 11

notice how it only works if the whole thing is in parenthesis, like (2a-b)^2, not (2a)^2-b, or (2a-b^2), neither of those work. But do notice, that something like
(x^4-1) can be factored as
(x^2-1)(x^2+1)=(x+1)(x-1)(x^2+1)

Answer 12

O i see! thank you!

Answer 13

No problem :)