Compute: 217^2 + 183^2.

Given data

• Evaluate 217^2 + 183^2.

Concept / Approach

• Use (a + b)^2 = a^2 + 2ab + b^2 \u2192 a^2 + b^2 = (a + b)^2 − 2ab.
• Since 217 + 183 = 400, this choice simplifies arithmetic.

Step-by-step calculation

a + b = 217 + 183 = 400 \u2192 (a + b)^2 = 400^2 = 160000ab = 217 \u00d7 183 = (200 + 17)(200 − 17) = 200^2 − 17^2 = 40000 − 289 = 39711a^2 + b^2 = (a + b)^2 − 2ab = 160000 − 2 \u00d7 39711 = 160000 − 79422 = 80578

Verification

217^2 = 47089; 183^2 = 33489; sum = 47089 + 33489 = 80578.

Common pitfalls

• Computing ab incorrectly; the product shortcut (x + y)(x − y) helps avoid errors.

Final Answer

80578