Finite Math Examples

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

Step 1

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = y$ .

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x - y$ and $y - x$ .

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Step 2.1.1

Factor $- 1$ out of $x$ .

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

Step 2.1.2

Factor $- 1$ out of $- y$ .

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

Step 2.1.3

Factor $- 1$ out of $- 1 (- x) - (y)$ .

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

Step 2.1.4

Reorder terms.

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

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

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

Step 2.2

Rewrite $- 1 (x^{2} + x y + y^{2})$ as $- (x^{2} + x y + y^{2})$ .

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

Step 2.3

Apply the distributive property.

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