Find the Perfect Square Trinomial (x+3y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $3$ by $3$ .

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

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

Move $y$ .

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

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

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