Solve 81k^4t^6-144

$$81 k ^ { 4 } t ^ { 6 } - 144$$

Factor

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

Solution Steps

Factor out 9.

$$9\left(9k^{4}t^{6}-16\right)$$

Consider 9k^{4}t^{6}-16. Rewrite 9k^{4}t^{6}-16 as \left(3k^{2}t^{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).

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

Rewrite the complete factored expression.

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

Evaluate

$$81k^{4}t^{6}-144$$