Solve {l}{225x^{4}+25m^{2}n^{4}-150x^2m^2}{x^2+2x(x-y)+(x-y)^2}

$$\left. \begin{array} { l } { 225 x ^ { 4 } + 25 m ^ { 2 } n ^ { 4 } - 150 x ^ { 2 } m ^ { 2 } } \\ { x ^ { 2 } + 2 x ( x - y ) + ( x - y ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$25\left(2x-y\right)^{2}\left(9x^{4}+m^{2}n^{4}-6\left(mx\right)^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$225x^{4}+25m^{2}n^{4}-150x^{2}m^{2}=25\left(9x^{4}-6m^{2}x^{2}+m^{2}n^{4}\right)$$

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

$$25\left(2x-y\right)^{2}\left(9x^{4}-6m^{2}x^{2}+m^{2}n^{4}\right)$$

Expand the expression.

$$900x^{6}-600m^{2}x^{4}-150m^{2}x^{2}y^{2}+100m^{2}x^{2}n^{4}-100xym^{2}n^{4}+225y^{2}x^{4}+25m^{2}y^{2}n^{4}-900yx^{5}+600ym^{2}x^{3}$$

Evaluate

$$25\left(9x^{4}+m^{2}n^{4}-6\left(mx\right)^{2}\right),\ \left(2x-y\right)^{2}$$