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

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

Step 1

Expand $(2 x^{2} + 3 x y - y^{2}) (x + 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $3$ by $2$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$2 x^{3} + 6 x^{2} + 3 x^{2} y + 9 x y - y^{2} x - y^{2} \cdot 3$

Multiply $3$ by $- 1$ .

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

Simplify the expression.

Move $y^{2}$ .

$2 x^{3} + 6 x^{2} + 3 x^{2} y + 9 x y - 1 x y^{2} - 3 y^{2}$

Move $6 x^{2}$ .

$2 x^{3} + 3 x^{2} y + 9 x y - 1 x y^{2} - 3 y^{2} + 6 x^{2}$

Move $9 x y$ .

$2 x^{3} + 3 x^{2} y - 1 x y^{2} - 3 y^{2} + 9 x y + 6 x^{2}$

Move $2 x^{3}$ .

$3 x^{2} y - 1 x y^{2} + 2 x^{3} - 3 y^{2} + 9 x y + 6 x^{2}$

Reorder $3 x^{2} y$ and $- 1 x y^{2}$ .

$- 1 x y^{2} + 3 x^{2} y + 2 x^{3} - 3 y^{2} + 9 x y + 6 x^{2}$