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 $3$ .

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