Find the Product (x+2y)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

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 $3$ .

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