# How do you multiply using the distributive property 5(31)?

Aug 6, 2018

$5 \left(31\right) = 155$

#### Explanation:

Multiplication is both left-distributive and right-distributive over addition.

That is, for any $a$, $b$ and $c$ we have:

$a \left(b + c\right) = a b + a c \text{ }$ left distributive

$\left(a + b\right) c = a c + b c \text{ }$ right distributive

We can use left distributivity to make the example product easier to calculate, finding:

$5 \left(31\right) = 5 \left(30 + 1\right) = 5 \left(30\right) + 5 \left(1\right) = 150 + 5 = 155$