Question

Could someone please factor this?

x^2+4x+4-4y^2
Please show work in your answer, thank you. :)

Answer 1

(x+2+2y)(x+2-2y)

Explanation:

Start with the given expression: x^2 + 4x + 4 - 4y^2.

Group the first three terms together and leave the last term separate:

x^2 + 4x + 4 - 4y^2.

Notice that the first three terms form a perfect square trinomial: (x + 2)^2.

Rewrite the expression using the perfect square trinomial:

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

Recognize that this is now the difference of squares: (a^2 - b^2) = (a + b)(a - b).

In our case, a = (x + 2) and b = 2y.

Apply the difference of squares formula:

(x + 2 + 2y)(x + 2 - 2y).

Therefore, the fully factored form of the expression x^2 + 4x + 4 - 4y^2 is:

(x + 2 + 2y)(x + 2 - 2y).