Solve t^3+3t^2+9t,2t^2(t^2-9)

$$t ^ { 3 } + 3 t ^ { 2 } + 9 t , 2 t ^ { 2 } ( t ^ { 2 } - 9 )$$

Least Common Multiple

$$2t^{2}\left(t^{2}-9\right)\left(t^{2}+3t+9\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2t^{2}\left(t^{2}-9\right)=2\left(t-3\right)\left(t+3\right)t^{2}$$

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

$$2\left(t-3\right)\left(t+3\right)t^{2}\left(t^{2}+3t+9\right)$$

Expand the expression.

$$2t^{6}+6t^{5}-54t^{3}-162t^{2}$$

Evaluate

$$t\left(t^{2}+3t+9\right),2t^{2}\left(t^{2}-9\right)$$