```Question 117895
{{{2((3(m-5)+18)-(3(5m-3)+4))}}}

This is just an exercise in the application of the Distributive, Associative, and Commutative Properties:

Distributive Property: {{{a(b +c)=ab+ac}}} for all real a, b, and c.
Associative Property: {{{(a+b)+c=a+(b+c)}}} for all real a, b, and c.
Commutative Property: {{{a+b=b+a}}} for all real a and b.

For this problem you need to work from the inside and go out.  Start with the {{{3(m-5)}}} part.  Using the distributive property, you can write that as {{{3m-15}}}.  Same thing for the {{{3(5m-3)}}} part, which can be written as {{{15m-9}}}.  Put these two expressions back into the original expression:

{{{2((3m-15)+18-(15m-9)+4))}}}

Now remove the parentheses around {{{-(15m-9)}}} by distributing the minus sign.  Think of the minus sign in front of a set of parentheses as a -1, and then apply the distributive property.  You end up with {{{-15m+9}}}.  Put this back into the expression.

{{{2((3m-15)+18-15m+9+4)}}}

Next you can remove the parentheses from the {{{(3m-15)}}} without changing anything else because there is no minus sign in front of this quantity.

{{{2(3m-15+18-15m+9+4)}}}

For the expression that is still inside of the parentheses, you have 2 terms that contain the variable m, and 4 terms that are just numbers.  Add up all the like terms so that you get {{{-12m}}} and {{{+16}}}.  This is where we are applying the Associative and Commutative Properties.

{{{2(-12m+16)}}}

One last application of the Distributive Property and we are done:

{{{-24m+32}}}, or it might be more neatly put {{{32-24m}}}

Hope that helps.  I hope you and your family have a joyous holiday season.
John```