Solve {l}{5xy-10x-3y+6}{n^2-m^2+6m-9}

$$\left. \begin{array} { l } { 5 x y - 10 x - 3 y + 6 } \\ { n ^ { 2 } - m ^ { 2 } + 6 m - 9 } \end{array} \right.$$

Least Common Multiple

$$\left(y-2\right)\left(5x-3\right)\left(\left(3-m\right)^{2}-n^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$n^{2}-\left(-3+m\right)^{2}=\left(m+n-3\right)\left(-m+n+3\right)$$

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

$$\left(y-2\right)\left(3-n-m\right)\left(5x-3\right)\left(n-m+3\right)$$

Expand the expression.

$$5xym^{2}-5xyn^{2}-30mxy+45xy+10xn^{2}-10xm^{2}+60mx-90x+3yn^{2}-3ym^{2}+18my-27y-6n^{2}+6m^{2}-36m+54$$

Evaluate

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