Evaluate
r^{20}+r^{10}+1
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r^{20}+r^{10}+1
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\frac{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)}{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)}
Factor the expressions that are not already factored.
\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)
Cancel out \left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right) in both numerator and denominator.
r^{20}+r^{10}+1
Expand the expression.
\frac{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)}{\left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right)}
Factor the expressions that are not already factored.
\left(r^{10}-r^{5}+1\right)\left(r^{10}+r^{5}+1\right)
Cancel out \left(r-1\right)\left(r+1\right)\left(r^{4}-r^{3}+r^{2}-r+1\right)\left(r^{4}+r^{3}+r^{2}+r+1\right) in both numerator and denominator.
r^{20}+r^{10}+1
Expand the expression.
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