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 sum 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: 25x^{4}-5x^{2}+1,5x^{2}+1.
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