Find the Product (3x+y)^2

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

Rewrite ${(3 x + y)}^{2}$ as $(3 x + y) (3 x + y)$ .

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

Expand $(3 x + y) (3 x + y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$9 x^{2} + 3 x y + y (3 x) + y \cdot y$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 x y + 3 y x + y \cdot y$

Multiply $y$ by $y$ .

$9 x^{2} + 3 x y + 3 y x + y^{2}$

Add $3 x y$ and $3 y x$ .

Move $y$ .

$9 x^{2} + 3 x y + 3 x y + y^{2}$

Add $3 x y$ and $3 x y$ .

$9 x^{2} + 6 x y + y^{2}$