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Home / p^3 + q^3 = (p+q)(p^2 - pq + q^2)

p^3 + q^3 = (p+q)(p^2 - pq + q^2)

February 22, 2026

p^3 + q^3 = (p+q)(p^2 - pq + q^2)

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\boxed{\frac{4(\sqrt{x} - 2)}{x - 4}}
Question:** A patent attorney is reviewing a patent that involves a formula where \( p+q=10 \) and \( p^2+q^2=58 \). Find \( p^3 + q^3 \).
We know the identity:
Given \( p+q = 10 \) and \( p^2 + q^2 = 58 \), we first find \( pq \) using:
10^2 = 58 + 2pq
= 58 + 2pq

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