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q^{3}+1
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q^{3}+1
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\frac{\left(q-1\right)\left(q+1\right)\left(-q^{2}+q-1\right)\left(q^{2}+q+1\right)}{\left(q-1\right)\left(-q^{2}-q-1\right)}
Factor the expressions that are not already factored.
\frac{-\left(q-1\right)\left(q+1\right)\left(-q^{2}+q-1\right)\left(-q^{2}-q-1\right)}{\left(q-1\right)\left(-q^{2}-q-1\right)}
Extract the negative sign in 1+q+q^{2}.
-\left(q+1\right)\left(-q^{2}+q-1\right)
Cancel out \left(q-1\right)\left(-q^{2}-q-1\right) in both numerator and denominator.
q^{3}+1
Expand the expression.
\frac{\left(q-1\right)\left(q+1\right)\left(-q^{2}+q-1\right)\left(q^{2}+q+1\right)}{\left(q-1\right)\left(-q^{2}-q-1\right)}
Factor the expressions that are not already factored.
\frac{-\left(q-1\right)\left(q+1\right)\left(-q^{2}+q-1\right)\left(-q^{2}-q-1\right)}{\left(q-1\right)\left(-q^{2}-q-1\right)}
Extract the negative sign in 1+q+q^{2}.
-\left(q+1\right)\left(-q^{2}+q-1\right)
Cancel out \left(q-1\right)\left(-q^{2}-q-1\right) in both numerator and denominator.
q^{3}+1
Expand the expression.
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