Question

Show step-by-step solution on how to factor 4x^2-y^2+4y-4

Answer 1

Is the last one -4x or -4?

Answer 2

-4

Answer 3

i actually already have the answer, it's (2x+y-2)(2x-y+2) i just don't know how to arrive at that answer

Answer 4

Factoring by Grouping:

4x^2-y^2+4y-4 =

4x^2 - (y^2 -4y + 4)

@elleblythe Do you agree so far?

Answer 5

-1 was factored out as a common monomial factor from -y^2+4y-4 to get
4x^2 - (y^2 -4y + 4)

Answer 6

@elleblythe Waiting for your response.

Answer 7

@Directrix actually i arrived at that solution also but if -(y^2+4y-4) is factored, won't it become -(y-2)^2? which will then become (2x-y-2)(2x+y-2), so it's still different from (2x+y-2)(2x-y+2)?

Answer 8

-(y^2+4y-4) will become -(y-2)^2, a perfect square trinomial.

Because you are that far along on the problem, I'll post the solution so that you can view and ask questions.

Answer 9

4x^2 - (y^2 -4y + 4)

Perfect Square Trinomial

4 x ^2 - (y-2)^2

Difference of Two Squares

[4 x ^2 - (y-2)^2]

[2x + (y-2)] [2x - (y-2)]

[2x + y -2] [2x - y + 2] --> factorization

Answer 10

Questions? @elleblythe

Answer 11

@Directrix thanks for clearing that up for me!

Answer 12

Alrighty, you are welcome.