Solve 3a^4-48

$$3 a ^ { 4 } - 48$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(a^{4}-16\right)$$

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

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

Consider a^{2}-4. Rewrite a^{2}-4 as a^{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).

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

Rewrite the complete factored expression. Polynomial a^{2}+4 is not factored since it does not have any rational roots.

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

Evaluate

$$3\left(a^{4}-16\right)$$