Simplify (x+y)^2

${(x + y)}^{2}$

Step 1

Rewrite ${(x + y)}^{2}$ as $(x + y) (x + y)$ .

$(x + y) (x + y)$

Step 2

Expand $(x + y) (x + y)$ using the FOIL Method.

Apply the distributive property.

$x (x + y) + y (x + y)$

Apply the distributive property.

$x \cdot x + x y + y (x + y)$

Apply the distributive property.

$x \cdot x + x y + y x + y \cdot y$

$x \cdot x + x y + y x + y \cdot y$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x y + y x + y \cdot y$

Multiply $y$ by $y$ .

$x^{2} + x y + y x + y^{2}$

$x^{2} + x y + y x + y^{2}$

Add $x y$ and $y x$ .

Reorder $y$ and $x$ .

$x^{2} + x y + x y + y^{2}$

Add $x y$ and $x y$ .

$x^{2} + 2 x y + y^{2}$

$x^{2} + 2 x y + y^{2}$

$x^{2} + 2 x y + y^{2}$

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