Simplify 3(x+y)^2

$3 {(x + y)}^{2}$

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

$3 ((x + y) (x + y))$

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

Apply the distributive property.

$3 (x (x + y) + y (x + y))$

Apply the distributive property.

$3 (x \cdot x + x y + y (x + y))$

Apply the distributive property.

$3 (x \cdot x + x y + y x + y \cdot y)$

$3 (x \cdot x + x y + y x + y \cdot y)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x y + y x + y \cdot y)$

Multiply $y$ by $y$ .

$3 (x^{2} + x y + y x + y^{2})$

$3 (x^{2} + x y + y x + y^{2})$

Add $x y$ and $y x$ .

Reorder $y$ and $x$ .

$3 (x^{2} + x y + x y + y^{2})$

Add $x y$ and $x y$ .

$3 (x^{2} + 2 x y + y^{2})$

$3 (x^{2} + 2 x y + y^{2})$

$3 (x^{2} + 2 x y + y^{2})$

Apply the distributive property.

$3 x^{2} + 3 (2 x y) + 3 y^{2}$

Multiply $2$ by $3$ .

$3 x^{2} + 6 x y + 3 y^{2}$

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