Solve 256a^3+4b^3

$$256 a ^ { 3 } + 4 b ^ { 3 }$$

Factor

$$4\left(4a+b\right)\left(16a^{2}-4ab+b^{2}\right)$$

Solution Steps

Factor out 4.

$$4\left(64a^{3}+b^{3}\right)$$

Consider 64a^{3}+b^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

$$\left(4a+b\right)\left(16a^{2}-4ab+b^{2}\right)$$

Rewrite the complete factored expression.

$$4\left(4a+b\right)\left(16a^{2}-4ab+b^{2}\right)$$

Evaluate

$$4\left(64a^{3}+b^{3}\right)$$