Solve 32x^4-2a^4quad=

$$32 x ^ { 4 } - 2 a ^ { 4 } \quad =$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(16x^{4}-a^{4}\right)$$

Consider 16x^{4}-a^{4}. Rewrite 16x^{4}-a^{4} as \left(4x^{2}\right)^{2}-\left(a^{2}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

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

$$\left(2x-a\right)\left(2x+a\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$32x^{4}-2a^{4}$$