Solve y^3+2y^2-81y-162

$$y ^ { 3 } + 2 y ^ { 2 } - 81 y - 162$$

Factor

$$\left(y-9\right)\left(y+2\right)\left(y+9\right)$$

Solution Steps

Do the grouping y^{3}+2y^{2}-81y-162=\left(y^{3}+2y^{2}\right)+\left(-81y-162\right), and factor out y^{2} in the first and -81 in the second group.

$$y^{2}\left(y+2\right)-81\left(y+2\right)$$

Factor out common term y+2 by using distributive property.

$$\left(y+2\right)\left(y^{2}-81\right)$$

Consider y^{2}-81. Rewrite y^{2}-81 as y^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-9\right)\left(y+9\right)$$

Rewrite the complete factored expression.

$$\left(y-9\right)\left(y+2\right)\left(y+9\right)$$

Evaluate

$$\left(y+2\right)\left(y^{2}-81\right)$$