Solve 36x^2-25x^6x^4

$$36 { x }^{ 2 } -25 { x }^{ 6 } { x }^{ 4 }$$

Factor

$$x^{2}\left(-5x^{4}-6\right)\left(5x^{4}-6\right)$$

Solution Steps

Factor out x^{2}.

$$x^{2}\left(36-25x^{4}x^{4}\right)$$

Consider 36-25x^{8}. Rewrite 36-25x^{8} as 6^{2}-\left(5x^{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).

$$\left(6-5x^{4}\right)\left(6+5x^{4}\right)$$

Reorder the terms.

$$\left(-5x^{4}+6\right)\left(5x^{4}+6\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -5x^{4}+6,5x^{4}+6.

$$x^{2}\left(-5x^{4}+6\right)\left(5x^{4}+6\right)$$

Evaluate

$$x^{2}\left(36-25x^{8}\right)$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$36x^{2}-25x^{10}$$