Solution: We use the identity \( p^3 + q^3 = (p + q)^3 - 3pq(p + q) \). First, compute \( pq \) using \( (p + q)^2 = p^2 + 2pq + q^2 \). Substituting, \( 10^2 = 58 + 2pq \) gives \( 100 = 58 + 2pq \), so \( pq = 21 \). Then, \( p^3 + q^3 = 10^3 - 3 \cdot 21 \cdot 10 = 1000 - 630 = 370 \). oxed{370}

Sat, 18 Apr 2026 07:40:14 +0000

Content under review