16Hit1600
Advanced MathVery hardUsing a difference of squares to find a sum

Advanced Math practice question

If x² − y² = 40 and x − y = 4, what is the value of x + y?

Answer: 10

x² − y² = (x − y)(x + y). So 40 = 4(x + y), giving x + y = 10. (Here x = 7 and y = 3.)

Common wrong answers

If you answered 36
36 is 40 − 4, subtracting instead of using the factored form (x − y)(x + y).
If you answered 44
44 is 40 + 4. The relationship is multiplicative: 4 × (x + y) = 40.
If you answered 160
160 is 40 × 4, multiplying instead of dividing.

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