Solve 12a^4-48x^2=

$$12 a ^ { 4 } - 48 x ^ { 2 } =$$

Factor

$$12\left(a^{2}-2x\right)\left(2x+a^{2}\right)$$

Solution Steps

Factor out 12.

$$12\left(a^{4}-4x^{2}\right)$$

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

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

Reorder the terms.

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

Rewrite the complete factored expression.

$$12\left(-2x+a^{2}\right)\left(2x+a^{2}\right)$$

Evaluate

$$12\left(a^{4}-4x^{2}\right)$$