Solve {l}{25m^{4}-10m^{2}n+n^2}{9p^4+6p^2q+q^2}

$$\left. \begin{array} { l } { 25 m ^ { 4 } - 10 m ^ { 2 } n + n ^ { 2 } } \\ { 9 p ^ { 4 } + 6 p ^ { 2 } q + q ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(\left(5m^{2}-n\right)\left(3p^{2}+q\right)\right)^{2}$$

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.

$$\left(5m^{2}-n\right)^{2}\left(3p^{2}+q\right)^{2}$$

Expand the expression.

$$225m^{4}p^{4}+9n^{2}p^{4}+n^{2}q^{2}-90nm^{2}p^{4}-10nm^{2}q^{2}-60nqm^{2}p^{2}+25q^{2}m^{4}+6qn^{2}p^{2}+150qp^{2}m^{4}$$

Evaluate

$$\left(5m^{2}-n\right)^{2},\ \left(3p^{2}+q\right)^{2}$$