Solve 27x^6-243y^6

$$27 x ^ { 6 } - 243 y ^ { 6 }$$

Factor

$$27\left(x^{3}-3y^{3}\right)\left(x^{3}+3y^{3}\right)$$

Solution Steps

Factor out 27.

$$27\left(x^{6}-9y^{6}\right)$$

Consider x^{6}-9y^{6}. Rewrite x^{6}-9y^{6} as \left(x^{3}\right)^{2}-\left(3y^{3}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x^{3}-3y^{3}\right)\left(x^{3}+3y^{3}\right)$$

Rewrite the complete factored expression.

$$27\left(x^{3}-3y^{3}\right)\left(x^{3}+3y^{3}\right)$$

Evaluate

$$27\left(x^{6}-9y^{6}\right)$$