#[Distributive Law for Real Numbers][Ley distributiva para los números reales]#

#[If $a,$ $b,$ and $c$ are any real numbers, then:][Si $a, b,$ y $c$ son cualquieras números reales, entonces:]#

#[Law][Ley]#	Examples
$a(b \pm c) = ab \pm ac$ #[Left distributive law][Ley distributiva izquierda]#	$x(x+1)$\t = $x(x) + x(1) $ \\ \t ${}=x^2 + x$ $x^3(y-x)$\t ${}= x^3(y) - x^3(x) $ \\ \t ${}=x^3y - x^4$ $-7(x+y+z)$ ${}= (-7)x + (-7)y + (-7)z$ * ${}=-7x - 7y - 7z$ $\dfrac{4x^2}{3y}\left(\dfrac{xy^2}{2z} - \dfrac{y}{x}\right)$ ${}= \dfrac{4x^2}{3y}\left(\dfrac{xy^2}{2z}\right) - \dfrac{4x^2}{3y}\left(\dfrac{y}{x}\right)$ ${}= \dfrac{4x^2\cdot xy^2}{3y\cdot 2z} - \dfrac{4x^2\cdot y}{3y\cdot x}$ #[Rule for multiplying fractions][Relga para multiplicar fracciones]# ${}= \dfrac{4x^3y^2}{6yz} - \dfrac{4x^2y}{3xy}$ #[Rules for exponents][Relgas para exponentes]# ${}= \dfrac{2x^3y}{3z} - \dfrac{4x}{3}$
$(a \pm b)c = ac \pm bc$ #[Right distributive law][Ley distributiva derecha]#	$(x+1)y$\t ${}=x(y) + 1(y) $ \\ \t ${}=xy + y$ $(1-3x+x^2)x$ ${}=1(x) - 3x(x) + x^2(x)$ ${}=x - 3x^2 + x^3$ $\left(\dfrac{xy^2}{2z} + \dfrac{2y}{3x}\right)\dfrac{z}{xy^2}$ ${}= \dfrac{xy^2}{2z}\left(\dfrac{z}{xy^2}\right) + \dfrac{2y}{3x}\left(\dfrac{z}{xy^2}\right)$ ${}= \dfrac{xy^2\cdot z}{2z\cdot xy^2} + \dfrac{2y\cdot z}{3x\cdot xy^2}$ #[Rule for multiplying fractions][Relga para multiplicar fracciones]# ${}= \dfrac{xy^2z}{2xy^2z} + \dfrac{2yz}{3x^2y^2}$ #[Rules for exponents][Relgas para exponentes]# ${}= \dfrac{1}{2} + \dfrac{2z}{3x^2y}$