Solve m^2-n^2+2n-1=

$$m ^ { 2 } - n ^ { 2 } + 2 n - 1 =$$

Factor

$$\left(m+n-1\right)\left(m-n+1\right)$$

Solution Steps

Rewrite as difference of two terms.

$$m^{2}-\left(n^{2}-2n+1\right)$$

Rewrite the terms as squares.

$$m^{2}-\left(1-n\right)^{2}$$

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

$$\left(m-1+n\right)\left(m+1-n\right)$$

Evaluate

$$-\left(n-1\right)^{2}+m^{2}$$