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What is the value of (x + y)(x + y) if xy = -3 and x² + y² = 10?

A.      1
B.       2
C.      3
D.      4

First we have to use the FOIL method for multiplying binomials.  

Using that, (x + y)(x + y) becomes x² + 2xy + y².

If x² + y² = 10, and xy = -3,

then (x² + y²) + 2(xy) = 10 + 2(-3),

or 10 – 6, which is 4.

The answer is (D).

source:  math.rice.edu