Question

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)`?

Answer 1

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 .

Answer 2

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*(x/5)` can be expanded to `(24/5)*x` , or `4.8*x` and `17*(x*8)` expands to `17*x*8 = 136*x`
Similarly, with addition `10*(3+x)` expands to `30 +10*x` and `25*(x-4)` expands to `25*x - 100`

Answer 3

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(x+3)` there are TWO terms inside the bracket, while:

In `5(x xx 3)` there is only ONE term inside the bracket.

Removing the bracket in each case gives the following:

`5(x+3) = 5x+15" but "5(x xx 3) = 5(3x) = 15x`

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

While with `x xx 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 `xx` 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(x div 5) = 24 xx x/5 = (24x)/5`

`17(x xx 8) = 17xx x xx 8 = 136x`

I hope this helps?