This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Formula for a^3 + b^3 a^3 + b^3 = (a + b)(a^2 - ab + b^2) Step 2: Formula for a^2 + b^2 a^2 + b^2 = (a + b)^2 - 2ab Substitute a + b = 10 and ab = 21: a^2 + b^2 = 10^2 - 2 × 21 = 100 - 42 = 58 Step 3: Substitute into the expression for a^2 - ab + b^2 a^2 - ab + b^2 = a^2 + b^2 - ab = 58 - 21 = 37 Step 4: Substitute into the formula for a^3 + b^3 a^3 + b^3 = (a + b)(a^2 - ab + b^2) = 10 × 37 = 370 Final answer: 370