$a \times (b+c)$ $\,=\,$ $a \times b + a \times c$

An arithmetic property that distributes the multiplication across the addition is called the distributive property of multiplication over addition.

$a$, $b$ and $c$ are three literals and represent three terms.

The product of the term $a$ and the sum of the terms $b$ and $c$ is written in mathematical form as follows.

$a \times (b+c)$

The product of them can be evaluated by distributing the multiplication over the addition.

$\implies$ $a \times (b+c)$ $\,=\,$ $a \times b + a \times c$

This distributive property can also be used to distribute the multiplication of a term over the sum of two or more terms.

$\implies$ $a \times (b+c+d+\ldots)$ $\,=\,$ $a \times b + a \times c + a \times d + \ldots$

Learn how to prove the distributive property of multiplication across addition in algebraic form by geometric method.

$2$, $3$ and $4$ are three numbers. Find the product of number $2$ and sum of the numbers of $3$ and $4$.

$2 \times (3+4)$

Find the value of this arithmetic expression.

$\implies$ $2 \times (3+4)$ $\,=\,$ $2 \times 7$

$\implies$ $2 \times (3+4) \,=\, 14$

Now, find the sum of the products of $2$ and $3$, and $2$ and $4$.

$2 \times 3 + 2 \times 4$ $\,=\,$ $6+8$

$\implies$ $2 \times 3 + 2 \times 4$ $\,=\,$ $14$

Now, compare the results of both expressions. They are equal.

$\,\,\, \therefore \,\,\,\,\,\,$ $2 \times (3+4)$ $\,=\,$ $2 \times 3 + 2 \times 4$ $\,=\,$ $14$

Latest Math Topics

Latest Math Problems

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved