If x + y = 9 and xy = 14, what is the value of (x-y)²?

Use the identity $(x - y)^2 = (x + y)^2 - 4xy$. It follows from $(x+y)^2 = x^2 + 2xy + y^2$ and $(x-y)^2 = x^2 - 2xy + y^2$, whose difference is $4xy$. Substitute: $9^2 - 4(14) = 81 - 56 = 25$. Check: the numbers solve $t^2 - 9t + 14 = 0$, so they are 2 and 7, and $(2 - 7)^2 = 25$. A common wrong answer is 53, which comes from using $x^2 + y^2$ instead: $81 - 28 = 53$. Another is 67, from subtracting $xy$ only once: $81 - 14$. The factor is 4, not 2 or 1.