Solve 4a^4-36

$$4 a ^ { 4 } - 36$$

Factor

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

Solution Steps

Factor out 4.

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

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

$$\left(a^{2}-3\right)\left(a^{2}+3\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: a^{2}-3,a^{2}+3.

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

Evaluate

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