a^3 + b^3 = 1000 - 3(21)(10) = 1000 - 630 = 370

Mon, 04 May 2026 13:17:33 +0000

Understanding the Equation: a³ + b³ = 1000 – 3(21)(10) = 370 – A Step-by-Step Breakdown Mathematics often disguises elegant patterns within seemingly complex expressions, and one such case arises in the equation a³ + b³ = 1000 – 3(21)(10) = 370. At first glance, this equation may appear abstract, but with a little algebra and number sense, we uncover a powerful insight rooted in algebraic identities. ### The Given Equation:
a³ + b³ = 1000 – 3(21)(10) = 370
This simplifies to:
a³ + b³ = 370 ### The Mathematical Identity: Sum of Cubes
The left-hand side of the equation, a³ + b³, is a classic algebraic form governed by the identity:
a³ + b³ = (a + b)(a² – ab + b²)
However, in this instance, instead of factoring further, we start by computing the right-hand side:
1000 – 3 × 21 × 10 = 1000 – 630 = 370
So, we confirm:
a³ + b³ = 370