Solve 3c^4-48

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

Factor

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

Solution Steps

Factor out 3.

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

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

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

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

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

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

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

Evaluate

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