If the sum of two numbers is 16 and their difference is 3, find x² − y².

Correct answer: 48. x² − y² = (x + y)(x − y) = 16 × 3 = 48.

Background: This uses the difference-of-squares identity, x² − y² = (x + y)(x − y), so you do not need to find x and y.

• 2: 2 does not equal 16 × 3.
• 20: 20 does not equal 16 × 3.
• 25: 25 does not equal 16 × 3.

Did you know? The same identity helps with quick mental sums such as 99² − 1² = 100 × 98.

Memory trick: Sum × Difference = 16 × 3 = 48.