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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Step 3

Simplify each term.

Multiply $5$ by $3$ .

$15 x^{3} y + 3 x^{2} y (2 y) + 3 x y^{3} \cdot 3$

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

Move $y$ .

$15 x^{3} y + 3 x^{2} (y \cdot y) \cdot 2 + 3 x y^{3} \cdot 3$

Multiply $y$ by $y$ .

$15 x^{3} y + 3 x^{2} y^{2} \cdot 2 + 3 x y^{3} \cdot 3$

Multiply $2$ by $3$ .

$15 x^{3} y + 6 x^{2} y^{2} + 3 x y^{3} \cdot 3$

Multiply $3$ by $3$ .

$15 x^{3} y + 6 x^{2} y^{2} + 9 x y^{3}$