Solve 2a^9+54b^12

$$2 a ^ { 9 } + 54 b ^ { 12 }$$

Factor

$$2\left(a^{3}+3b^{4}\right)\left(a^{6}-3a^{3}b^{4}+9b^{8}\right)$$

Solution Steps

Factor out 2.

$$2\left(a^{9}+27b^{12}\right)$$

Consider a^{9}+27b^{12}. Rewrite a^{9}+27b^{12} as \left(a^{3}\right)^{3}+\left(3b^{4}\right)^{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).

$$\left(a^{3}+3b^{4}\right)\left(a^{6}-3a^{3}b^{4}+9b^{8}\right)$$

Rewrite the complete factored expression.

$$2\left(a^{3}+3b^{4}\right)\left(a^{6}-3a^{3}b^{4}+9b^{8}\right)$$

Evaluate

$$2\left(a^{9}+27b^{12}\right)$$