Solve 16x^6-2x^3+1/16

$$16 { x }^{ 6 } -2 { x }^{ 3 } + \frac{ 1 }{ 16 }$$

Factor

$$\frac{\left(16x^{3}-1\right)^{2}}{16}$$

Solution Steps

Factor out \frac{1}{16}.

$$\frac{256x^{6}-32x^{3}+1}{16}$$

Consider 256x^{6}-32x^{3}+1. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=16x^{3} and b=1.

$$\left(16x^{3}-1\right)^{2}$$

Rewrite the complete factored expression. Polynomial 16x^{3}-1 is not factored since it does not have any rational roots.

$$\frac{\left(16x^{3}-1\right)^{2}}{16}$$

Evaluate

$$\frac{\left(16x^{3}-1\right)^{2}}{16}$$