Solve 3/64-243x^4

$$\frac { 3 } { 64 } - 243 x ^ { 4 }$$

Factor

$$\frac{3\left(-72x^{2}-1\right)\left(72x^{2}-1\right)}{64}$$

Solution Steps

Factor out \frac{3}{64}.

$$\frac{3\left(1-5184x^{4}\right)}{64}$$

Consider 1-5184x^{4}. Rewrite 1-5184x^{4} as 1^{2}-\left(72x^{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).

$$\left(1-72x^{2}\right)\left(1+72x^{2}\right)$$

Reorder the terms.

$$\left(-72x^{2}+1\right)\left(72x^{2}+1\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -72x^{2}+1,72x^{2}+1.

$$\frac{3\left(-72x^{2}+1\right)\left(72x^{2}+1\right)}{64}$$

Evaluate

$$\frac{3}{64}-243x^{4}$$