Solve {l}{5(p+2q+r)}{6(p+q-2r)}

$$\left. \begin{array} { l } { 5 ( p + 2 q + r ) } \\ { 6 ( p + q - 2 r ) } \end{array} \right.$$

Least Common Multiple

$$-30\left(p+q-2r\right)\left(p+2q+r\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$5p+10q+5r=5\left(p+2q+r\right) 6p+6q-12r=6\left(p+q-2r\right)$$

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

$$-30\left(p+q-2r\right)\left(p+2q+r\right)$$

Expand the expression.

$$-30p^{2}-90pq+30pr-60q^{2}+90qr+60r^{2}$$

Evaluate

$$5\left(p+2q+r\right),\ 6\left(p+q-2r\right)$$