Solve {l}{text{(a)}2m^2-3mm+n^2}{text{(b)}2m^2-3mm+n^2-10m+5n}

$$\left. \begin{array} { l } { \text { (a) } 2 m ^ { 2 } - 3 m m + n ^ { 2 } } \\ { \text { (b) } 2 m ^ { 2 } - 3 m m + n ^ { 2 } - 10 m + 5 n } \end{array} \right.$$

Least Common Multiple

$$\left(2am^{2}-3m^{2}+n^{2}\right)\left(2bm^{2}-3m^{2}-10m+n^{2}+5n\right)$$

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.

$$\left(2am^{2}-3m^{2}+n^{2}\right)\left(2bm^{2}-3m^{2}-10m+n^{2}+5n\right)$$

Expand the expression.

$$4abm^{4}-6am^{4}-6bm^{4}+9m^{4}-20am^{3}+30m^{3}+2am^{2}n^{2}+2bm^{2}n^{2}-6m^{2}n^{2}-10mn^{2}+n^{4}+5n^{3}+10anm^{2}-15nm^{2}$$

Evaluate

$$2am^{2}-3m^{2}+n^{2},\ 2bm^{2}-3m^{2}-10m+n^{2}+5n$$