Solve x^2-y^2+4y-4

$$x ^ { 2 } - y ^ { 2 } + 4 y - 4$$

Factor

$$\left(x+y-2\right)\left(x-y+2\right)$$

Solution Steps

Rewrite as difference of two terms.

$$x^{2}-\left(y^{2}-4y+4\right)$$

Rewrite the terms as squares.

$$x^{2}-\left(2-y\right)^{2}$$

The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2+y\right)\left(x+2-y\right)$$

Evaluate

$$-\left(y-2\right)^{2}+x^{2}$$