Solve {l}{x^{2}-y^{2}-x+2xy-y^2}{m^2+2mn+n^2-p^2+2x}

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

Least Common Multiple

$$\left(x^{2}+2xy-x-2y^{2}\right)\left(\left(m+n\right)^{2}-p^{2}+2x\right)$$

Solution Steps

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x^{2}+2xy-x-2y^{2}\right)\left(2x+2mn+m^{2}+n^{2}-p^{2}\right)$$

Expand the expression.

$$2x^{3}+m^{2}x^{2}+n^{2}x^{2}+2mnx^{2}-p^{2}x^{2}-2x^{2}-4xy^{2}+4mnxy+2xym^{2}+2xyn^{2}-2xyp^{2}+xp^{2}-2mnx-xm^{2}-xn^{2}+2p^{2}y^{2}-4mny^{2}-2m^{2}y^{2}-2n^{2}y^{2}+4yx^{2}$$

Evaluate

$$x^{2}+2xy-x-2y^{2},\ \left(m+n\right)^{2}-p^{2}+2x$$