# Distributive Property

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One of the properties of real numbers is distributive property, also known as distributivity of multiplication over addition. It is used to solve variable expression which is in the form of $a(b+c)$ and the like.

The property says, for any $a,b,c \in \mathbb{R}, a(b+c)=ab+ac$.

Examples:

1. $2(x+y)=2x+2y$
2. $-3(2a+b-c)=-3(2a)-3(b)-3(-c)=-6a-3b+3c$
3. $3(2x+3y)=3(2x)+3(2y)=6x+9y$

One of the real conveniences of algebra is the use of parentheses to indicate that certain operations are to be performed. When we do the operations that are indicated, we say "we remove parentheses." For example, the expression $3(2x+3y)-4(2x-y)$ indicates that 4 times the binomial $2x-y$ is to be subtracted from 3 times the binomial $2x+3y$. Hence,

$3(2x+3y)-4(2x-y)=6x+6y-8x+4y=-2x+10y$