16Hit 1600
Advanced MathVery hardProduct from a sum and a difference

Advanced Math practice question

For numbers x and y, x + y = 9 and x − y = 5. Using the identity (x + y)² − (x − y)² = 4xy, what is the value of xy?

Answer: 14

(x + y)² − (x − y)² = 81 − 25 = 56 = 4xy, so xy = 14.

Common wrong answers

If you answered 7
7 is x itself (x = 7, y = 2); the product is 14.
If you answered 28
Divide 56 by 4, not by 2.
If you answered 56
56 is 4xy; divide by 4.

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