Simplify 2xy(x^3-3y^2)

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Multiply $x^{3}$ by $x$ .

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

$2 (x^{3} x^{1}) y + 2 x y (- 3 y^{2})$

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

$2 x^{3 + 1} y + 2 x y (- 3 y^{2})$

Add $3$ and $1$ .

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

Step 3

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

Move $y^{2}$ .

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

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

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

$2 x^{4} y + 2 x (y^{2} y^{1}) \cdot - 3$

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

$2 x^{4} y + 2 x y^{2 + 1} \cdot - 3$

Add $2$ and $1$ .

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

Step 4

Multiply $- 3$ by $2$ .

$2 x^{4} y - 6 x y^{3}$