Solve 9y^7-144y

$$9 y ^ { 7 } - 144 y$$

Factor

$$9y\left(y^{3}-4\right)\left(y^{3}+4\right)$$

Solution Steps

Factor out 9.

$$9\left(y^{7}-16y\right)$$

Consider y^{7}-16y. Factor out y.

$$y\left(y^{6}-16\right)$$

Consider y^{6}-16. Rewrite y^{6}-16 as \left(y^{3}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y^{3}-4\right)\left(y^{3}+4\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: y^{3}-4,y^{3}+4.

$$9y\left(y^{3}-4\right)\left(y^{3}+4\right)$$

Evaluate

$$9y\left(y^{6}-16\right)$$