Simplify (x+y)(x-y)(x+y)

$(x + y) (x - y) (x + y)$

Expand $(x + y) (x - y)$ using the FOIL Method.

Apply the distributive property.

$(x (x - y) + y (x - y)) (x + y)$

Apply the distributive property.

$(x \cdot x + x (- y) + y (x - y)) (x + y)$

Apply the distributive property.

$(x \cdot x + x (- y) + y x + y (- y)) (x + y)$

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- y) + y x + y (- y)$ .

Reorder the factors in the terms $x (- y)$ and $y x$ .

$(x \cdot x - x y + x y + y (- y)) (x + y)$

Add $- x y$ and $x y$ .

$(x \cdot x + 0 + y (- y)) (x + y)$

Add $x \cdot x$ and $0$ .

$(x \cdot x + y (- y)) (x + y)$

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Expand $(x^{2} - y^{2}) (x + y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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 $1$ .

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

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

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

Add $2$ and $1$ .

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

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $y^{2}$ .

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

Simplify (x+y)(x-y)(x+y)

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