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)#?

3 Answers
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

Answer:

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#

Jun 3, 2017

Answer:

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?