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q^{3}\left(4q^{2}-25\right)
Factor out q^{3}.
\left(2q-5\right)\left(2q+5\right)
Consider 4q^{2}-25. Rewrite 4q^{2}-25 as \left(2q\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
q^{3}\left(2q-5\right)\left(2q+5\right)
Rewrite the complete factored expression.