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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Simplify by adding terms.

Combine the opposite terms in $x^{3} + x^{2} y + x^{2} y + x y^{2} - y^{2} x - y^{3}$ .

Reorder the factors in the terms $x y^{2}$ and $- y^{2} x$ .

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

Subtract $y^{2} x$ from $y^{2} x$ .

$x^{3} + x^{2} y + x^{2} y + 0 - y^{3}$

Add $x^{3} + x^{2} y + x^{2} y$ and $0$ .

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

Add $x^{2} y$ and $x^{2} y$ .

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