- Thread starter Keeyn
- Start date

- Joined
- Nov 12, 2017

- Messages
- 3,012

Once you have expanded 3(x+4) + 2(x+3) to (3x+12) + (2x+6), the parentheses are no longer required; the result is equivalent to 3x+12+2x+6. That is, for any value of x, the two expressions have the same value.

You appear to be thinking that the parts of the expression retain some invisible link to their origin; they don't. As long as two expressions always have the same value, they are equivalent, no matter what you have done to get from one to the other.

Or perhaps you are just wondering about the difference between (3x+12)(2x+6) and(3x+12) + (2x+6). The reason you can drop parentheses in the latter is that all the operations connecting the terms are additions, so the associative property of addition applies. That is not true in the former, where we have a mix of additions and multiplication, and the distributive property applies.

Note that if we couldn't write 3x+12+2x+6, we couldn't then rearrange (using the commutative property) and combine like terms (using the distributive property). This step of dropping parentheses is essential to what we are typically doing in algebra.

- Joined
- Nov 12, 2017

- Messages
- 3,012

I don't think I can tell you

I hope I made it clear in my response to you that the step with parentheses

Actually, in your new example (which is considerably trickier than the first), there are many other steps that might be shown, if one wanted to show every detail:

3(x + 4) - 6(3 + x)

3(x + 4) + -[6(3 + x]

3(x + 4) + -1[6(3 + x)]

3(x + 4) + (-1*6)(3 + x)

3(x + 4) + (-6)(3 + x)

[3*x + 3*4] + [(-6)3 + (-6)x]

[3x + 12] + [-18 + -6x]

3x + 12 + -18 + -6x

3x + -6x + 12 + -18

(3 + -6)x + (12 + -18)

-3x + -6

-3x - 6

I would never write out all those steps; but that is what I am actually doing in simplifying the expression. We

The trouble is that any teacher of a group of students (and especially any author writing to many students they will never even see) can't know what each of them does or does not already know, and therefore will make some choices that are not suitable for all of them.

That's part of the reason I prefer tutoring individually. But even then, I have to find out what you are ready for by trying things out and seeing what results I get.

But back to your question, no, it is not your imagination. The step exists; it is just one that teachers may easily assume students can figure out for themselves.

- Joined
- Apr 14, 2018

- Messages
- 3

So, after you use your distributive properties. The parenthesis are removed and you must combine "Like Terms" therefore if you have an equation 3(x+2)+2(x+2), you first use distributive properties which would equal

3x+6+2x+4. So now you have 2 separate "like terms" 1) just numbers and 2)coefficient of the variable "x".

So, you would combine 3x+2x and 6+4. Which would result in 5x+10. At this point you can no longer "pair down" the variables or numbers.