Simplify -2xy(2y+4x^2)

$- 2 x y (2 y + 4 x^{2})$

Step 1

Apply the distributive property.

$- 2 x y (2 y) - 2 x y (4 x^{2})$

Step 2

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Step 3

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$- 2 x y^{2} \cdot 2 - 2 (x^{2} x^{1}) y \cdot 4$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 x y^{2} \cdot 2 - 2 x^{2 + 1} y \cdot 4$

Add $2$ and $1$ .

$- 2 x y^{2} \cdot 2 - 2 x^{3} y \cdot 4$

Step 4

Simplify each term.

Multiply $2$ by $- 2$ .

$- 4 x y^{2} - 2 x^{3} y \cdot 4$

Multiply $4$ by $- 2$ .

$- 4 x y^{2} - 8 x^{3} y$