Solve {l}{m^2-x^2-2m}{+2xy+1-y^2}

$$\left. \begin{array} { l } { m ^ { 2 } - x ^ { 2 } - 2 m } \\ { + 2 x y + 1 - y ^ { 2 } } \end{array} \right.$$

Factor

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

Solution Steps

Rewrite m^{2}-x^{2}-2m+2xy+1-y^{2} as \left(-1+m\right)^{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).

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

Reorder the terms.

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

Evaluate

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