Solve {l}{3q^2+20q+14}{6r^3y+4r^2y-10t}

$$\left. \begin{array} { l } { 3 q ^ { 2 } + 20 q + 14 } \\ { 6 r ^ { 3 } y + 4 r ^ { 2 } y - 10 t } \end{array} \right.$$

Least Common Multiple

$$2\left(3q^{2}+20q+14\right)\left(5t-2yr^{2}-3yr^{3}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$3q^{2}+20q+14=3\left(q-\left(-\frac{1}{3}\sqrt{58}-\frac{10}{3}\right)\right)\left(q-\left(\frac{1}{3}\sqrt{58}-\frac{10}{3}\right)\right) 6r^{3}y+4r^{2}y-10t=2\left(3yr^{3}+2yr^{2}-5t\right)$$

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

$$2\left(3q^{2}+20q+14\right)\left(5t-2yr^{2}-3yr^{3}\right)$$

Expand the expression.

$$-18yq^{2}r^{3}-12yq^{2}r^{2}-120qyr^{3}-80qyr^{2}-84yr^{3}-56yr^{2}+30tq^{2}+200qt+140t$$

Evaluate

$$3q^{2}+20q+14,\ 6yr^{3}+4yr^{2}-10t$$