Solve 3r^3-81f^3

$$3 r ^ { 3 } - 81 f ^ { 3 }$$

Factor

$$3\left(r-3f\right)\left(r^{2}+3fr+9f^{2}\right)$$

Solution Steps

Factor out 3.

$$3\left(r^{3}-27f^{3}\right)$$

Consider r^{3}-27f^{3}. Rewrite r^{3}-27f^{3} as r^{3}-\left(3f\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(r-3f\right)\left(r^{2}+3fr+9f^{2}\right)$$

Rewrite the complete factored expression.

$$3\left(r-3f\right)\left(r^{2}+3fr+9f^{2}\right)$$

Evaluate

$$3\left(r^{3}-27f^{3}\right)$$