Solve {l}{(m+2)[(m^2+3m-6)+(m^2-2m+4)]}{[(t^2+3t-8)-(t^2-2t+6)](t-4)}

$$\left. \begin{array} { l } { ( m + 2 ) [ ( m ^ { 2 } + 3 m - 6 ) + ( m ^ { 2 } - 2 m + 4 ) ] } \\ { [ ( t ^ { 2 } + 3 t - 8 ) - ( t ^ { 2 } - 2 t + 6 ) ] ( t - 4 ) } \end{array} \right.$$

Least Common Multiple

$$\left(t-4\right)\left(5t-14\right)\left(m+2\right)\left(2m^{2}+m-2\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2m^{3}+5m^{2}-4=2\left(m+2\right)\left(m^{2}+\frac{1}{2}m-1\right) -34t+56+5t^{2}=\left(t-4\right)\left(5t-14\right)$$

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

$$2\left(t-4\right)\left(5t-14\right)\left(m+2\right)\left(m-\frac{-\sqrt{17}-1}{4}\right)\left(m-\frac{\sqrt{17}-1}{4}\right)$$

Expand the expression.

$$112m^{3}+25m^{2}t^{2}+280m^{2}+10t^{2}m^{3}-20t^{2}-68tm^{3}-170tm^{2}+136t-224$$

Evaluate

$$\left(m+2\right)\left(2m^{2}+m-2\right),\ \left(t-4\right)\left(5t-14\right)$$