Solve x^10/4-x^12y^8/36=

$$\frac { x ^ { 10 } } { 4 } - \frac { x ^ { 12 } y ^ { 8 } } { 36 } =$$

Factor

$$\frac{\left(-xy^{4}-3\right)\left(xy^{4}-3\right)x^{10}}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{9x^{10}-x^{12}y^{8}}{36}$$

Consider 9x^{10}-x^{12}y^{8}. Factor out x^{10}.

$$x^{10}\left(9-x^{2}y^{8}\right)$$

Consider 9-x^{2}y^{8}. Rewrite 9-x^{2}y^{8} as 3^{2}-\left(-xy^{4}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3+xy^{4}\right)\left(3-xy^{4}\right)$$

Reorder the terms.

$$\left(xy^{4}+3\right)\left(-xy^{4}+3\right)$$

Rewrite the complete factored expression.

$$\frac{x^{10}\left(xy^{4}+3\right)\left(-xy^{4}+3\right)}{36}$$

Evaluate

$$-\frac{y^{8}x^{12}}{36}+\frac{x^{10}}{4}$$