Solve 3x^8-27x^6

$$3 x ^ { 8 } - 27 x ^ { 6 }$$

Factor

$$3\left(x-3\right)\left(x+3\right)x^{6}$$

Solution Steps

Factor out 3.

$$3\left(x^{8}-9x^{6}\right)$$

Consider x^{8}-9x^{6}. Factor out x^{6}.

$$x^{6}\left(x^{2}-9\right)$$

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

$$\left(x-3\right)\left(x+3\right)$$

Rewrite the complete factored expression.

$$3x^{6}\left(x-3\right)\left(x+3\right)$$

Evaluate

$$3\left(x^{2}-9\right)x^{6}$$