Solve 2a^4-8

$$2 a ^ { 4 } - 8$$

Factor

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

Solution Steps

Factor out 2.

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

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

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

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

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

Evaluate

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