$a \times (b-c)$ $\,=\,$ $a \times b -a \times c$
An arithmetic property that distributes the multiplication across the subtraction is called the distributive property of multiplication over subtraction.
$a$, $b$ 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.
$\implies$ $a \times (b-c)$ $\,=\,$ $a \times b -a \times c$
Learn how to prove the distributive property of multiplication across subtraction in algebraic form by geometrical method.
$3$, $4$ 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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