Solve 144-a^6

$$144 - a ^ { 6 }$$

Factor

$$\left(-a^{3}-12\right)\left(a^{3}-12\right)$$

Solution Steps

Rewrite 144-a^{6} as 12^{2}-\left(-a^{3}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(12+a^{3}\right)\left(12-a^{3}\right)$$

Reorder the terms. The following polynomials are not factored since they do not have any rational roots: -a^{3}+12,a^{3}+12.

$$\left(a^{3}+12\right)\left(-a^{3}+12\right)$$

Evaluate

$$144-a^{6}$$