Competition - post a photo you've taken of nature >>

C2 - Why does only one bracket become negative, not all 3? (Factorising)

Why do they only make one bracket negative (they change 3x-7) to 7-3x? Why doesn't the negative sign end up making all of the brackets negative, so it'd be (-x-3)(7-3x)(-1-2x)?

And why do they change that bracket so it's negative and not one of the others?

Can you please explain this to me?

Thanks

Reply 1

username3991332

Either way is correct.

An example. If you had something, let's say:

-1 \times 69 \times 420 \times 9001

=-69 \times 420 \times 9001

=-69 \times (-1 \times -420) \times (-1 \times -9001)

= -69 \times (-1 \times -1) \times -420 \times -9001

=-69 \times -420 \times -9001

Reply 2

stuart4

Original post by Mathematicat

Either way is correct.

An example. If you had something, let's say:

-1 \times 69 \times 420 \times 9001

=-69 \times 420 \times 9001

=-69 \times (-1 \times -420) \times (-1 \times -9001)

= -69 \times (-1 \times -1) \times -420 \times -9001

=-69 \times -420 \times -9001

Okay, I think i'm with you. But why have they (and the mark scheme) chosen to make the (3x-7) bracket negative so it turns to (7-3x)? Why not do it to one of the other two?

The mark scheme only mentions either of those two forms in the image I posted - it doesn't mention about having something like (-x-3)(3x-7)(2x+1), could you do that instead?

Reply 3

username3991332

Original post by stuart4

Doing it to all of the brackets is usually unnecessary. The markscheme probably says something along the lines of 'or equivalent'. Well either way it's correct.

Reply 4

Prasiortle

Original post by stuart4

Original post by Mathematicat

Either way is correct.

An example. If you had something, let's say:

-1 \times 69 \times 420 \times 9001

=-69 \times 420 \times 9001

=-69 \times (-1 \times -420) \times (-1 \times -9001)

= -69 \times (-1 \times -1) \times -420 \times -9001

=-69 \times -420 \times -9001

Original post by stuart4

Original post by Mathematicat

Doing it to all of the brackets is usually unnecessary. The markscheme probably says something along the lines of 'or equivalent'. Well either way it's correct.

No, everything written in this thread up to this point has been completely wrong. Consider e.g. -(-3)*(-7): applying the negative sign to both brackets would give 3*7=21, when the answer should be -21. Think of the negative sign as just a -1 multiplying whatever's in front of it. Since multiplication is commutative (can be done in any order), you can apply a single negative sign to any single factor/bracket, and in your example, they chose to apply it to (3x-7), since if they were to apply it to e.g. (x+1), you would get (-x-1), which would be correct but looks ugly as it contains two negative signs.

Reply 5

MR1999

Original post by stuart4

Because -(abc)=-1*(abc). Now multiplication is associative and commutative so it doesn't matter where you place the brackets nor does the order, but you have to understand that there's only one -1, so you can have -1*a(bc) or a(-1*b)c or ab(-1*c) but nothing more than that because you only have a single -1 on the outside. What the others are saying is wrong but works in this case because we have an odd number of terms and -1*(2n+1)=-1.

Reply 6

Cat?

Original post by username3991332

Doing it to all of the brackets is usually unnecessary.

Original post by Prasiortle

No, everything written in this thread up to this point has been completely wrong.

No, you misinterpreted what I said. By "either way is correct" specially applied to this example. However, I never said it was true in general for any number of brackets which is something I should of made more clear as I mean't "all" as 'all three'.

-a \times b \times c

= -a \times -b \times -c

Is what I was trying to show. So it works in this case but is pointless.

(edited 5 years ago)

Reply 7

Prasiortle

Original post by Luminescence0

-a \times b \times c

= -a \times -b \times -c

Is what I was trying to show. So it works in this case but is pointless.

Sure, the wrong way happens to give the right answer because the number of brackets is odd. That doesn't change the fact that it's extremely poor pedagogy to even mention this at all, when you could have just stated the right way to do it and avoided any mention of this wrong way. Now, since the OP sees that the wrong way can work sometimes, they are more likely to continue using it and thus to get further questions wrong in the future.

Reply 8

monkeyman0121

lets say you have: -(x+2)(x+3)(x+4)

You can make any bracket times by minus. But not all of them. That would be wrong. What you have seen at the top of the thread is wrong. It may produce the same answer but that is only because 3 minuses make a minus overall just like 1 minus. If you had 2 brackets then it would be totally different if you times both by -.

Reply 9

Cat?

Original post by Prasiortle

OP asked why one bracket was multiplied by -1 and not the rest of them and I answered that either way in this example is correct but doing it his way is unnecessary. I was hoping post #2 would have shown that it depends with the number of -1s being multiplied together to give 1.
As I've said, I should of been more clear. I will own up to the mistake.

Reply 10

Cat?

Original post by monkeyman0121

Read the rest of the thread.

Reply 11

monkeyman0121

Original post by Luminescence0

Read the rest of the thread.

So I can't have my input just because something has already been said? I mean more people saying the same thing really does reinforce the fact that the thing they are all saying is more often right than wrong?

Reply 12

Cat?

Original post by monkeyman0121

I thought you didn't read the entire thread because you repeated exactly what somebody else already said. :smile:

Reply 13

monkeyman0121

Original post by Luminescence0

I thought you didn't read the entire thread because you repeated exactly what somebody else already said. :smile:

Nah I noticed I just thought more proof is better. If I was a thread creator I would want consistency from most of the posters so that I know what is probably right. :tongue: