# Distributive property of Multiplication over Subtraction

## Formula

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

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

### Introduction

$a$, $b$ and $c$ are three literals and denote three terms in algebraic form.

The product of the term $a$ and the difference of the terms $b$ and $c$ can be written in the following mathematical form.

$a \times (b-c)$

The product of them can be calculated by distributing the multiplication over the subtraction.

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

### Proof

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

#### Verification

$3$, $4$ and $7$ are three numbers. Find the product of number $2$ and subtraction of $4$ from $7$.

$3 \times (7-4)$

Now, calculate the value of the arithmetic expression.

$\implies$ $3 \times (7-4)$ $\,=\,$ $3 \times 3$

$\implies$ $3 \times (7-4) \,=\, 9$

Now, find the difference of the products of $3$ and $4$, and $3$ and $7$.

$3 \times 7 -3 \times 4$ $\,=\,$ $21-12$

$\implies$ $3 \times 7 -3 \times 4$ $\,=\,$ $9$

Now, compare the results of both the arithmetic expressions. Numerically, they are equal.

$\,\,\, \therefore \,\,\,\,\,\,$ $3 \times (7-4)$ $\,=\,$ $3 \times 7 -3 \times 4$ $\,=\,$ $9$

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