Evaluating a function

If f(x) = x² + 3, then f(x + y) = ?
A.)  x² + 2xy + y² + 3
B.)  x² + 2xy + y²
C.)  x² + 2xy + 3
D.)  x² + 3 + y
E.)  x² + y²

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If f(x) = x² + 3,
then f(x+ y)
=  (x + y)² + 3   {substituted (x + y), in for x, into f(x) = x² + 3}
=  (x + y)(x + y) + 3    {when squaring a binomial, multiply it by itself}
=  x² + 2xy + y² + 3   {used FOIL method / distributive property to multiply}

A.)  x² + 2xy + y² + 3

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