Find the Product (x-y)(x^2+xy+y^2)

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

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

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

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

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

Move $y^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

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

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

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

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

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

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

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

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

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

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

Add $x^{3}$ and $0$ .

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

Find the Product (x-y)(x^2+xy+y^2)

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