Solve 9y^3+63y^2-y-7

$$9 y ^ { 3 } + 63 y ^ { 2 } - y - 7$$

Factor

$$\left(3y-1\right)\left(y+7\right)\left(3y+1\right)$$

Solution Steps

Do the grouping 9y^{3}+63y^{2}-y-7=\left(9y^{3}+63y^{2}\right)+\left(-y-7\right), and factor out 9y^{2} in the first and -1 in the second group.

$$9y^{2}\left(y+7\right)-\left(y+7\right)$$

Factor out common term y+7 by using distributive property.

$$\left(y+7\right)\left(9y^{2}-1\right)$$

Consider 9y^{2}-1. Rewrite 9y^{2}-1 as \left(3y\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3y-1\right)\left(3y+1\right)$$

Rewrite the complete factored expression.

$$\left(3y-1\right)\left(3y+1\right)\left(y+7\right)$$

Evaluate

$$\left(y+7\right)\left(9y^{2}-1\right)$$