Solve 8x^6y^2-18x^2y^2

$$8 x ^ { 6 } y ^ { 2 } - 18 x ^ { 2 } y ^ { 2 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(4x^{6}y^{2}-9x^{2}y^{2}\right)$$

Consider 4x^{6}y^{2}-9x^{2}y^{2}. Factor out x^{2}y^{2}.

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

Consider 4x^{4}-9. Rewrite 4x^{4}-9 as \left(2x^{2}\right)^{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).

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

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 2x^{2}-3,2x^{2}+3.

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

Evaluate

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