# What property is shown in the equation jk+jl=j(k+l)?

Oct 28, 2016

(Left) distribution of multiplication over addition.

#### Explanation:

There are two forms of the distributive property:

• $a \left(b + c\right) = a b + a c \text{ }$ Multiplication is left distributive over addition.

• $\left(a + b\right) c = a c + b c \text{ }$ Multiplication is right distributive over addition.

If we also know that multiplication is commutative then we need only specify one of these. The other follows.

For example, using the left distributive property, we can prove the right distributive property as follows:

$\left(a + b\right) c = c \left(a + b\right) \text{ }$ since multiplication is commutative

$\textcolor{w h i t e}{\left(a + b\right) c} = c a + c b \text{ }$ using the left distributive property

$\textcolor{w h i t e}{\left(a + b\right) c} = a c + b c \text{ }$ using commutativity (twice)

So in contexts where multiplication is commutative, we often don't bother to specify left or right distributive. We just say that multiplication is distributive over addition.