Factor
\left(5x^{2}-1\right)\left(25x^{4}+5x^{2}+1\right)
Evaluate
125x^{6}-1
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\left(5x^{2}-1\right)\left(25x^{4}+5x^{2}+1\right)
Rewrite 125x^{6}-1 as \left(5x^{2}\right)^{3}-1^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right). The following polynomials are not factored since they do not have any rational roots: 5x^{2}-1,25x^{4}+5x^{2}+1.
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