Solve a^2-b^2-2b-1

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

Factor

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

Solution Steps

Rewrite as difference of two terms.

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

Rewrite the terms as squares.

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

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

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

Evaluate

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