Solve 1-v^2-w^2+2vw=

$$1 - v ^ { 2 } - w ^ { 2 } + 2 v w =$$

Factor

$$\left(v-w-1\right)\left(-v+w-1\right)$$

Solution Steps

Rewrite as difference of two terms.

$$1-\left(v^{2}+w^{2}-2vw\right)$$

Rewrite the terms as squares.

$$1^{2}-\left(v-w\right)^{2}$$

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

$$\left(1-v+w\right)\left(1+v-w\right)$$

Evaluate

$$-\left(v-w\right)^{2}+1$$