Solve 9y^4-9

$$9 y ^ { 4 } - 9$$

Factor

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

Solution Steps

Factor out 9.

$$9\left(y^{4}-1\right)$$

Consider y^{4}-1. Rewrite y^{4}-1 as \left(y^{2}\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).

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

Consider y^{2}-1. Rewrite y^{2}-1 as y^{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).

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

Rewrite the complete factored expression. Polynomial y^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

$$9\left(y^{4}-1\right)$$