# Does there have to be an addition or subtraction sign between numbers inside of a bracket in order for you to expand the bracket, or can it be a division or multiplication sign? For example, can you expand: 24 (x ÷ 5) or 17 (x xx 8)?

Jun 3, 2017

It can be addition or subtraction sign or it can be a division or multiplication sign as well, but order of operations would have to be PEMDAS i.e. Parentheses , Exponents , Multiplication and Division , and Addition and Subtraction .

Jun 3, 2017

No. There is a commutative and associative property for both multiplication and addition.

#### Explanation:

That means you can “expand” parenthetical statements by an external operation. In your examples,
$24 \cdot \left(\frac{x}{5}\right)$ can be expanded to $\left(\frac{24}{5}\right) \cdot x$ , or $4.8 \cdot x$ and $17 \cdot \left(x \cdot 8\right)$ expands to $17 \cdot x \cdot 8 = 136 \cdot x$
Similarly, with addition $10 \cdot \left(3 + x\right)$ expands to $30 + 10 \cdot x$ and $25 \cdot \left(x - 4\right)$ expands to $25 \cdot x - 100$

Jun 3, 2017

In order to expand by using the distributive law there has to be an addition or subtraction sign in the bracket.

#### Explanation:

If I understand you to mean the 'distributive law' for expanding, then you will only 'expand' the bracket if there is an addition or subtraction sign in the bracket.

In $5 \left(x + 3\right)$ there are TWO terms inside the bracket, while:

In $5 \left(x \times 3\right)$ there is only ONE term inside the bracket.

Removing the bracket in each case gives the following:

$5 \left(x + 3\right) = 5 x + 15 \text{ but } 5 \left(x \times 3\right) = 5 \left(3 x\right) = 15 x$

The reason for the expanding is that $x \mathmr{and} 3$ are unlike terms, so they cannot be added, but BOTH still need to be multiplied by $5$

While with $x \times 3$, they can be multiplied together and the product is then multiplied by the $5$

With the $+$ sign, the 5 is multiplied by both the $x$ and the $3$, but with the $\times$ sign, the 5 is multiplied once, because there is already a product inside the bracket.

Remember that there is a multiplication sign between the $5$ and the bracket.

$24 \left(x \div 5\right) = 24 \times \frac{x}{5} = \frac{24 x}{5}$

$17 \left(x \times 8\right) = 17 \times x \times 8 = 136 x$

I hope this helps?