Find the Product (3x+2y)^3

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

Use the Binomial Theorem.

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

Simplify each term.

Apply the product rule to $3 x$ .

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

Raise $3$ to the power of $3$ .

$27 x^{3} + 3 {(3 x)}^{2} (2 y) + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Rewrite using the commutative property of multiplication.

$27 x^{3} + 3 \cdot 2 {(3 x)}^{2} y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Multiply $3$ by $2$ .

$27 x^{3} + 6 {(3 x)}^{2} y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Apply the product rule to $3 x$ .

$27 x^{3} + 6 (3^{2} x^{2}) y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Raise $3$ to the power of $2$ .

$27 x^{3} + 6 (9 x^{2}) y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Multiply $9$ by $6$ .

$27 x^{3} + 54 x^{2} y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Multiply $3$ by $3$ .

$27 x^{3} + 54 x^{2} y + 9 x {(2 y)}^{2} + {(2 y)}^{3}$

Apply the product rule to $2 y$ .

$27 x^{3} + 54 x^{2} y + 9 x (2^{2} y^{2}) + {(2 y)}^{3}$

Rewrite using the commutative property of multiplication.

$27 x^{3} + 54 x^{2} y + 9 \cdot 2^{2} x y^{2} + {(2 y)}^{3}$

Raise $2$ to the power of $2$ .

$27 x^{3} + 54 x^{2} y + 9 \cdot 4 x y^{2} + {(2 y)}^{3}$

Multiply $9$ by $4$ .

$27 x^{3} + 54 x^{2} y + 36 x y^{2} + {(2 y)}^{3}$

Apply the product rule to $2 y$ .

$27 x^{3} + 54 x^{2} y + 36 x y^{2} + 2^{3} y^{3}$

Raise $2$ to the power of $3$ .

$27 x^{3} + 54 x^{2} y + 36 x y^{2} + 8 y^{3}$