Solve 81t^4-16

$$81 t ^ { 4 } - 16$$

Factor

$$\left(3t-2\right)\left(3t+2\right)\left(9t^{2}+4\right)$$

Solution Steps

Rewrite 81t^{4}-16 as \left(9t^{2}\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).

$$\left(9t^{2}-4\right)\left(9t^{2}+4\right)$$

Consider 9t^{2}-4. Rewrite 9t^{2}-4 as \left(3t\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3t-2\right)\left(3t+2\right)$$

Rewrite the complete factored expression. Polynomial 9t^{2}+4 is not factored since it does not have any rational roots.

$$\left(3t-2\right)\left(3t+2\right)\left(9t^{2}+4\right)$$

Evaluate

$$81t^{4}-16$$