Simplify (2xy^2)(x^2-5x+3y)

$(2 x y^{2}) (x^{2} - 5 x + 3 y)$

Apply the distributive property.

$2 x y^{2} x^{2} + 2 x y^{2} (- 5 x) + 2 x y^{2} (3 y)$

Simplify.

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

Move $x^{2}$ .

$2 (x^{2} x) y^{2} + 2 x y^{2} (- 5 x) + 2 x y^{2} (3 y)$

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

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

$2 (x^{2} x^{1}) y^{2} + 2 x y^{2} (- 5 x) + 2 x y^{2} (3 y)$

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

$2 x^{2 + 1} y^{2} + 2 x y^{2} (- 5 x) + 2 x y^{2} (3 y)$

Add $2$ and $1$ .

$2 x^{3} y^{2} + 2 x y^{2} (- 5 x) + 2 x y^{2} (3 y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 x^{3} y^{2} + 2 (x \cdot x) y^{2} \cdot - 5 + 2 x y^{2} (3 y)$

Multiply $x$ by $x$ .

$2 x^{3} y^{2} + 2 x^{2} y^{2} \cdot - 5 + 2 x y^{2} (3 y)$

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

Move $y$ .

$2 x^{3} y^{2} + 2 x^{2} y^{2} \cdot - 5 + 2 x (y \cdot y^{2}) \cdot 3$

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

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

$2 x^{3} y^{2} + 2 x^{2} y^{2} \cdot - 5 + 2 x (y^{1} y^{2}) \cdot 3$

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

$2 x^{3} y^{2} + 2 x^{2} y^{2} \cdot - 5 + 2 x y^{1 + 2} \cdot 3$

Add $1$ and $2$ .

$2 x^{3} y^{2} + 2 x^{2} y^{2} \cdot - 5 + 2 x y^{3} \cdot 3$

Simplify each term.

Multiply $- 5$ by $2$ .

$2 x^{3} y^{2} - 10 x^{2} y^{2} + 2 x y^{3} \cdot 3$

Multiply $3$ by $2$ .

$2 x^{3} y^{2} - 10 x^{2} y^{2} + 6 x y^{3}$