Solve 8a^6-64b^3

$$8 a ^ { 6 } - 64 b ^ { 3 }$$

Factor

$$8\left(a^{2}-2b\right)\left(a^{4}+4b^{2}+2ba^{2}\right)$$

Solution Steps

Factor out 8.

$$8\left(a^{6}-8b^{3}\right)$$

Consider a^{6}-8b^{3}. Rewrite a^{6}-8b^{3} as \left(a^{2}\right)^{3}-\left(2b\right)^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

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

Rewrite the complete factored expression.

$$8\left(a^{2}-2b\right)\left(a^{4}+4b^{2}+2ba^{2}\right)$$

Evaluate

$$8\left(a^{6}-8b^{3}\right)$$