Solve 16/25x^4-1/4

$$\frac{ 16 }{ 25 } { x }^{ 4 } - \frac{ 1 }{ 4 }$$

Factor

$$\frac{\left(8x^{2}-5\right)\left(8x^{2}+5\right)}{100}$$

Solution Steps

Factor out \frac{1}{100}.

$$\frac{64x^{4}-25}{100}$$

Consider 64x^{4}-25. Rewrite 64x^{4}-25 as \left(8x^{2}\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).

$$\left(8x^{2}-5\right)\left(8x^{2}+5\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 8x^{2}-5,8x^{2}+5.

$$\frac{\left(8x^{2}-5\right)\left(8x^{2}+5\right)}{100}$$

Evaluate

$$\frac{16x^{4}}{25}-\frac{1}{4}$$