Solve c^3-64c^2-9c+576

$$c ^ { 3 } - 64 c ^ { 2 } - 9 c + 576$$

Factor

$$\left(c-64\right)\left(c-3\right)\left(c+3\right)$$

Solution Steps

Do the grouping c^{3}-64c^{2}-9c+576=\left(c^{3}-64c^{2}\right)+\left(-9c+576\right), and factor out c^{2} in the first and -9 in the second group.

$$c^{2}\left(c-64\right)-9\left(c-64\right)$$

Factor out common term c-64 by using distributive property.

$$\left(c-64\right)\left(c^{2}-9\right)$$

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.

$$\left(c-64\right)\left(c-3\right)\left(c+3\right)$$

Evaluate

$$\left(c-64\right)\left(c^{2}-9\right)$$