Find the Product 3xy^2*(2xy+3y^2-cx^3)

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

Apply the distributive property.

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

Simplify.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Simplify each term.

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $3$ by $3$ .

$6 x^{2} y^{3} + 9 x y^{4} + 3 x^{4} y^{2} (- c)$

Multiply $- 1$ by $3$ .

$6 x^{2} y^{3} + 9 x y^{4} - 3 x^{4} y^{2} c$