Expert: Josh - 8/21/2009

Question
8 { [4 z - 2) +18] - [ 3 (4z-2) + 6] =

Answer
Dear Debra,

Whenever I see nested expressions, I always start simplifying things inside the inner-most bracket first, then work my way out from the deepest level of nesting.

I think a "(" is missing inside the first square bracket. Anyway, if we look at the expression inside the second square bracket, we have [3(4z-2)+6]. As a first step, we can multiply out 3(4z-2), this turns [3(4z-2)+6] into 12z-6+6 which simplifies to 12z.

I have just noticed that a closing curly bracket "}" is also missing. So, let's assume that the original expression reads as 8 { [4(z-2)+18] - [3(4z-2)+6] }

We do the same to [4(z-2)+18]. This part reduces to 4z-8+18 = 4z+10.

Now,  8 { [4(z-2)+18] - [3(4z-2)+6] } equals  8 { [4z+10] - [12z] }.
Next, we simplify the terms inside { }.

8 { [4(z-2)+18] - [3(4z-2)+6] }
= 8 { 4z+10 - 12z }
= 8 { -8z+10 } ...finally, multiply -8z+10 by 8
= -64z+80

Again, this only shows the order of expansion. No guarantee the answer is correct though as bits and pieces are missing from the original expression.