Solve 64a^4-1/16

$$64 a ^ { 4 } - \frac { 1 } { 16 }$$

Factor

$$\frac{\left(32a^{2}-1\right)\left(32a^{2}+1\right)}{16}$$

Solution Steps

Factor out \frac{1}{16}.

$$\frac{1024a^{4}-1}{16}$$

Consider 1024a^{4}-1. Rewrite 1024a^{4}-1 as \left(32a^{2}\right)^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(32a^{2}-1\right)\left(32a^{2}+1\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 32a^{2}-1,32a^{2}+1.

$$\frac{\left(32a^{2}-1\right)\left(32a^{2}+1\right)}{16}$$

Evaluate

$$64a^{4}-\frac{1}{16}$$