Evaluate: 753 × 753 + 247 × 247 − 753 × 247.

Given data

• a = 753, b = 247, with a + b = 1000.

Concept / Approach

• Rewrite a^2 + b^2 − ab via (a + b)^2: a^2 + b^2 = (a + b)^2 − 2ab ⇒ expression = (a + b)^2 − 3ab.

Step-by-step calculation

(a + b)^2 = 1000^2 = 1,000,000ab = 753 × 247 = 753 × (250 − 3) = 188,250 − 2,259 = 185,991Therefore, value = 1,000,000 − 3 × 185,991 = 1,000,000 − 557,973 = 442,027

Verification / Alternative

• Direct expansion a^2 + b^2 − ab matches the algebraic transformation result.

Final Answer

442027