Solve 48x^6-27x^2y^2

$$48 x ^ { 6 } - 27 x ^ { 2 } y ^ { 2 }$$

Factor

$$3x^{2}\left(4x^{2}-3y\right)\left(4x^{2}+3y\right)$$

Solution Steps

Factor out 3.

$$3\left(16x^{6}-9x^{2}y^{2}\right)$$

Consider 16x^{6}-9x^{2}y^{2}. Factor out x^{2}.

$$x^{2}\left(16x^{4}-9y^{2}\right)$$

Consider 16x^{4}-9y^{2}. Rewrite 16x^{4}-9y^{2} as \left(4x^{2}\right)^{2}-\left(3y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x^{2}-3y\right)\left(4x^{2}+3y\right)$$

Rewrite the complete factored expression.

$$3x^{2}\left(4x^{2}-3y\right)\left(4x^{2}+3y\right)$$

Evaluate

$$48x^{6}-27\left(xy\right)^{2}$$