Solve a^2-1-2x-x^2

$$a ^ { 2 } - 1 - 2 x - x ^ { 2 }$$

Factor

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

Solution Steps

Rewrite as difference of two terms.

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

Rewrite the terms as squares.

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

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

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

Evaluate

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