Question

can someone explain in words how 25(4a^2-4ab+b^2) = 25(2a-b)^2? thankyou!

Answer 1

25(4a^2-4ab+b^2)


25(4a^2-2ab-2ab+b^2)


25( 2a(2a-b)-b(2a-b) )


25(2a-b)(2a-b)


25(2a-b)^2

Answer 2

the key is to break up -4ab into -2ab-2ab and then you factor by grouping

Answer 3

notice how -2 and -2 both add to -4 (the middle coefficient) and multiply to 4 (the product of the first and last coefficients)

Answer 4

thank you so much!! i've spent lots of time just trying to understand that!
it completely cleared it up! thank you!!

Answer 5

np

Answer 6

the only thing im confused with is how you got from 25(4a^2-2ab-2ab+b^2) to 25( 2a(2a-b)-b(2a-b) ) ..

Answer 7

I factored 2a from 4a^2-2ab to get 2a(2a-b)


then I factored -b from -2ab+b^2 to get -b(2a-b)

Answer 8

alright but how come it is -b not +b

Answer 9

because I want to force the stuff leftover to be 2a-b


if I factored out b (and not -b), then I would get b(-2a+b)


but the -2a+b is NOT the same as 2a-b, so I can't factor that further

Answer 10

oh okay i see.
thanks a lot for the help!

Answer 11

yw