Solve 2a^4-2a^2

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

Factor

$$2\left(a-1\right)\left(a+1\right)a^{2}$$

Solution Steps

Factor out 2.

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

Consider a^{4}-a^{2}. Factor out a^{2}.

$$a^{2}\left(a^{2}-1\right)$$

Consider a^{2}-1. Rewrite a^{2}-1 as a^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(a-1\right)\left(a+1\right)$$

Rewrite the complete factored expression.

$$2a^{2}\left(a-1\right)\left(a+1\right)$$

Evaluate

$$2a^{2}\left(a^{2}-1\right)$$