Solve 16t^3-16

$$16 t ^ { 3 } - 16$$

Factor

$$16\left(t-1\right)\left(t^{2}+t+1\right)$$

Solution Steps

Factor out 16.

$$16\left(t^{3}-1\right)$$

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

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

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

$$16\left(t-1\right)\left(t^{2}+t+1\right)$$

Evaluate

$$16\left(t^{3}-1\right)$$