What is a² + b²?

Correct answer: c 5

a² + b² = {(a + b)² + (a − b)²}/2 = (6 + 4)/2 = 5.

Why the other options are wrong

• a 15: 15 does not come from the formula: (a + b)² + (a − b)² = 10, and half of that is 5.
• b 10: 6 + 4 = 10 is 2(a² + b²); it has not been halved.
• d 2: 2 = 6 − 4 is (a + b)² − (a − b)², which equals 4ab; a² + b² needs the sum instead, (6 + 4)/2 = 5.