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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

Subtract $x y$ from $x y$ .

$(x \cdot x + 0 - y \cdot y) (x^{2} + y^{2})$

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Step 3

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 4

Simplify terms.

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

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

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

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

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

Add $x^{2} x^{2}$ and $0$ .

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

Simplify each term.

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

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

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

Add $2$ and $2$ .

$x^{4} - y^{2} y^{2}$

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

Move $y^{2}$ .

$x^{4} - (y^{2} y^{2})$

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

$x^{4} - y^{2 + 2}$

Add $2$ and $2$ .

$x^{4} - y^{4}$

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

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