Evaluate (x-2y)^3

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

Use the Binomial Theorem.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $- 2$ .

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

Apply the product rule to $- 2 y$ .

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

Rewrite using the commutative property of multiplication.

$x^{3} - 6 x^{2} y + 3 \cdot {(- 2)}^{2} x y^{2} + {(- 2 y)}^{3}$

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

$x^{3} - 6 x^{2} y + 3 \cdot 4 x y^{2} + {(- 2 y)}^{3}$

Multiply $3$ by $4$ .

$x^{3} - 6 x^{2} y + 12 x y^{2} + {(- 2 y)}^{3}$

Apply the product rule to $- 2 y$ .

$x^{3} - 6 x^{2} y + 12 x y^{2} + {(- 2)}^{3} y^{3}$

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

$x^{3} - 6 x^{2} y + 12 x y^{2} - 8 y^{3}$