Question

1. which expression completes the identity $(x + y)^2 = \underline{\quad\quad\quad}$?

a $x^2 + 2xy + y^2$
b $(x - y)(x^2 + xy + y^2)$
c $(x + y)(x^2 - xy + y^2)$
d $(x + y)(x^2 - y^2)$

Explanation:

Step1: Expand the left-hand side

$(x+y)^2 = (x+y)(x+y)$

Step2: Distribute terms using FOIL

$(x+y)(x+y) = x^2 + xy + xy + y^2$

Step3: Combine like terms

$x^2 + xy + xy + y^2 = x^2 + 2xy + y^2$

Answer:

A. $x^2 + 2xy + y^2$