Solve 1/25-4/49x^4

$$\frac{ 1 }{ 25 } - \frac{ 4 }{ 49 } { x }^{ 4 }$$

Factor

$$\frac{\left(-10x^{2}-7\right)\left(10x^{2}-7\right)}{1225}$$

Solution Steps

Factor out \frac{1}{1225}.

$$\frac{49-100x^{4}}{1225}$$

Consider 49-100x^{4}. Rewrite 49-100x^{4} as 7^{2}-\left(10x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7-10x^{2}\right)\left(7+10x^{2}\right)$$

Reorder the terms.

$$\left(-10x^{2}+7\right)\left(10x^{2}+7\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -10x^{2}+7,10x^{2}+7.

$$\frac{\left(-10x^{2}+7\right)\left(10x^{2}+7\right)}{1225}$$

Evaluate

$$-\frac{4x^{4}}{49}+\frac{1}{25}$$