Solve {l}{v^2-7v+10quad(v-5)}{r^2+4n-12}

$$\left. \begin{array} { l } { v ^ { 2 } - 7 v + 10 \quad ( v - 5 ) } \\ { r ^ { 2 } + 4 n - 12 } \end{array} \right.$$

Least Common Multiple

$$\left(4n+r^{2}-12\right)\left(v^{2}+3v-50\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$v^{2}+3v-50=\left(v-\left(-\frac{1}{2}\sqrt{209}-\frac{3}{2}\right)\right)\left(v-\left(\frac{1}{2}\sqrt{209}-\frac{3}{2}\right)\right)$$

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

$$\left(4n+r^{2}-12\right)\left(v^{2}+3v-50\right)$$

Expand the expression.

$$4nv^{2}+12nv-200n+r^{2}v^{2}-50r^{2}-12v^{2}+3vr^{2}-36v+600$$

Evaluate

$$v^{2}+3v-50,\ 4n+r^{2}-12$$