Question

Question #60d6f

Answer 1

`(2-3x)^2`

Explanation:

`4-12x+9x^2 = (2)^2-2xx2xx3x+(3x)^2 = (2-3x)^2`

Answer 2

`(3x - 2)^2`

Explanation:

In order to factor `4-12x+9x^2`, it helps to rewrite the expression in standar form:

`9x^2-12x+4`

The goal is to do the FOIL method, only backwards. The first step is to write out the parenthesis where the factorization will go

`(" ")(" ")`

F - First
The first term is `9x^2`. There are a few different combinations of expressions that will multiply together to make `9x^2`:
`(9x" ")(x" ")`
`(3x" ")(3x" ")`
`(x" ")(9x" ")`

L - Last
The last term is `4`. This number also has factors:
`(" "1)(" "4)`
`(" "2)(" "2)`
`(" "4)(" "1)`

The question is, what combination of O - outer and I - Inner values, when multiplied, will add together to make -12? Without going through every possible variation, you may notice the outer values `3*2` plus the inner values `2*3` add together to make `12`.

`(3x" "2)(3x" "2)`

The only way to get a `-12` is if we add together `-6` and `-6`. To get negative sixes, we need to put negative values inside the factors.

`(3x - 2)(3x - 2)=(3x - 2)^2`