Solve {l}{5v(3v+7)-3(1-8v)}{15v^2+59v-3}{(3k-2)(2k+4)}

$$\left. \begin{array} { l } { 5 v ( 3 v + 7 ) - 3 ( 1 - 8 v ) } \\ { 15 v ^ { 2 } + 59 v - 3 } \\ { ( 3 k - 2 ) ( 2 k + 4 ) } \end{array} \right.$$

Least Common Multiple

$$2\left(3k-2\right)\left(k+2\right)\left(15v^{2}+59v-3\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$15v^{2}+59v-3=15\left(v-\left(-\frac{1}{30}\sqrt{3661}-\frac{59}{30}\right)\right)\left(v-\left(\frac{1}{30}\sqrt{3661}-\frac{59}{30}\right)\right) 15v^{2}+59v-3=15\left(v-\left(-\frac{1}{30}\sqrt{3661}-\frac{59}{30}\right)\right)\left(v-\left(\frac{1}{30}\sqrt{3661}-\frac{59}{30}\right)\right) 6k^{2}+8k-8=2\left(3k-2\right)\left(k+2\right)$$

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

$$2\left(3k-2\right)\left(k+2\right)\left(15v^{2}+59v-3\right)$$

Expand the expression.

$$90k^{2}v^{2}+120kv^{2}-120v^{2}+354vk^{2}+472kv-472v-18k^{2}-24k+24$$

Evaluate

$$15v^{2}+59v-3,\ 15v^{2}+59v-3,\ 6k^{2}+8k-8$$