# Mixing bracket types when writing solutions?

1. Sep 17, 2012

### trollcast

Is it okay to mix the types of brackets you use when writing out a solution to help make it a bit clearer?

For example:

If I was completeing the square with:

$$3x^{2} + 5x -2 = 0$$

I would factor out the 3 onto square brackets like this:

$3 \left[x^{2} + \frac{5}{3}x - \frac{2}{3} \right] = 0$

Then do my competing the square with round brackets:

$$3 \left[ \left( x + \frac{5}{6} \right)^{2} -\left(\frac{5}{6}\right)^{2} - \frac{2}{3} \right] = 0$$

Last edited: Sep 17, 2012
2. Sep 17, 2012

### micromass

Staff Emeritus
Yes, that is perfectly ok. It is even recommended.

Also, I think you made some calculations errors when completing the square.

3. Sep 17, 2012

### trollcast

Thanks,

There probably are errors as I was about ready to punch my tv trying to get latex to put in the brackets, turns out I had spelled right as rigt.

Edit: I think fixed the mistake.

4. Sep 17, 2012

### Staff: Mentor

In your example, I would divide both sides by 3, then you do not need the big brackets at all.
If that is not possible, [ ] are fine.

5. Sep 17, 2012

### trollcast

In some questions they ask for the answer in the form, $$a(x - b)^{2} + c$$

But yeah if I was just solving to find x I'd divide through, I probably have a few better examples here of where you could use multiple brackets but that was what came to mind first.

6. Sep 17, 2012

### dextercioby

If the question is indeed about 'bracketing' and not about completing the square, then I can only say that what you're doing is not right in my book, brackets 'evolve', as the expression gets more complicated. First you place a round bracket, then if you need to put a round bracket into the first round bracket, the initial round brackets become square. If furthermore, you need a new round bracket into the newly created round bracket, the square one will become a brace, the previously existing round bracket will become square. And more, well, the number of braces will increase, since we don't have new types anymore.

7. Sep 17, 2012

### Staff: Mentor

Maybe it's a British English vs. American English thing, but as I learned them, there are
• brackets - [] (AKA "square brackets", which IMO is redundant, since brackets already are square)
• braces - {} (AKA "curly" brackets)
• parentheses - () (AKA "round" brackets)

8. Sep 17, 2012

### dextercioby

Apparently Dirac called these things <> brackets, else he would not have coined the words bra for <| and ket for |>.

9. Sep 17, 2012

### Staff: Mentor

They're also called angle brackets. They're not normally used for grouping mathematical expressions, I don't believe.

10. Sep 17, 2012

### skiller

Not to mention those things that hold your trousers up.

11. Sep 17, 2012

### Staff: Mentor

Belts? :tongue:

12. Sep 17, 2012

### skiller

13. Sep 18, 2012

### Staff: Mentor

Can also embrace the use of different sized parenthesis pairs, e.g.,

23((4x + 5) - x(x + 1))