Solve 48x^12-75x^2

$$48 { x }^{ 12 } -75 { x }^{ 2 }$$

Factor

$$3x^{2}\left(4x^{5}-5\right)\left(4x^{5}+5\right)$$

Solution Steps

Factor out 3.

$$3\left(16x^{12}-25x^{2}\right)$$

Consider 16x^{12}-25x^{2}. Factor out x^{2}.

$$x^{2}\left(16x^{10}-25\right)$$

Consider 16x^{10}-25. Rewrite 16x^{10}-25 as \left(4x^{5}\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

$$3x^{2}\left(4x^{5}-5\right)\left(4x^{5}+5\right)$$

Evaluate

$$48x^{12}-75x^{2}$$