Evaluate (469 + 174)^2 − (469 − 174)^2.

Given data

• Expression: (a + b)^2 − (a − b)^2 with a = 469, b = 174.

Concept / Approach

• Use the identity: (a + b)^2 − (a − b)^2 = 4ab.

Step-by-step calculation

4ab = 4 × 469 × 174First compute 469 × 174 = 469×100 + 469×70 + 469×4 = 46900 + 32830 + 1876 = 81606Multiply by 4: 4 × 81606 = 326424

Alternative verification

Use difference of squares: (A^2 − B^2) = (A − B)(A + B)A = 469 + 174, B = 469 − 174 ⇒ (2×174)(2×469) = 4×174×469 (same result).

Common pitfalls

• Expanding both squares fully; identity is faster and less error-prone.

Final Answer

Value = 326424.