Solve 4-4x^2+8xy-4y^2

$$4 - 4 x ^ { 2 } + 8 x y - 4 y ^ { 2 }$$

Factor

$$4\left(x-y-1\right)\left(-x+y-1\right)$$

Solution Steps

Factor out 4.

$$4\left(1-x^{2}+2xy-y^{2}\right)$$

Consider 1-x^{2}+2xy-y^{2}. Rewrite as difference of two terms.

$$1-\left(x^{2}-2xy+y^{2}\right)$$

Rewrite the terms as squares.

$$1^{2}-\left(x-y\right)^{2}$$

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

$$\left(1-x+y\right)\left(1+x-y\right)$$

Reorder the terms.

$$\left(-x+y+1\right)\left(x-y+1\right)$$

Rewrite the complete factored expression.

$$4\left(-x+y+1\right)\left(x-y+1\right)$$

Evaluate

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