Divide (x^4-y^4)/(x-y)

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

Step 1

Simplify the numerator.

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\frac{{(x^{2})}^{2} - {(y^{2})}^{2}}{x - y}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = y^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

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

Step 2

Cancel the common factor of $x - y$ .

Cancel the common factor.

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

Divide $(x^{2} + y^{2}) (x + y)$ by $1$ .

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

Step 3

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.

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

Step 4

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.

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

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

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

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

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

Add $2$ and $1$ .

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

Divide (x^4-y^4)/(x-y)

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