Solve 6c^4-486

$$6 c ^ { 4 } - 486$$

Factor

$$6\left(c-3\right)\left(c+3\right)\left(c^{2}+9\right)$$

Solution Steps

Factor out 6.

$$6\left(c^{4}-81\right)$$

Consider c^{4}-81. Rewrite c^{4}-81 as \left(c^{2}\right)^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c^{2}-9\right)\left(c^{2}+9\right)$$

Consider c^{2}-9. Rewrite c^{2}-9 as c^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(c-3\right)\left(c+3\right)$$

Rewrite the complete factored expression. Polynomial c^{2}+9 is not factored since it does not have any rational roots.

$$6\left(c-3\right)\left(c+3\right)\left(c^{2}+9\right)$$

Evaluate

$$6\left(c^{4}-81\right)$$