Question

Factor by grouping:

4-12r+9r^2

i know the answer is (2-3r)^2

Can anyone explain to me how it is?

Answer 1

Because:

`(a-b)^2=a^2+2ab+b^2`

Answer 2

`(x-y)^2=x^2-2xy+y^2\\---------------------------\\\\4-12r+9r^2=2^2-2\cdot2\cdot3r+(3r)^2=(2-3r)^2`


`other\ method:\\\\4-12r+9r^2=4-6r-6r+9r^2=2(2-3r)-3r(2-3r)\\\\=(2-3r)(2-3r)=(2-3r)^2`