Multiplying by negative: don't understand why (x - 3)(x + 2) = (3 - x)(x + 2)

[DustinC]

My math book says (x - 3)(x + 2) is the same as -1(x - 3)(x + 2)

So if (x - 3)(x + 2) is the same as (3 - x)(x + 2).. Well I just don't get it.

I'd I substitute 6 for x in (x - 3) and (3 - x) the first one gives me 3 as an answer and the second gives me -3.

How can they both be the same?

 

[gregk]

My math book says (x - 3)(x + 2) is the same as -1(x - 3)(x + 2)

Did you make a mistake while typing this? As written it is wrong.

So if (x - 3)(x + 2) is the same as (3 - x)(x + 2).. Well I just don't get it.

I'd I substitute 6 for x in (x - 3) and (3 - x) the first one gives me 3 as an answer and the second gives me -3.

How can they both be the same?

\(\displaystyle (x-3)\) and \(\displaystyle (3-x)\) are not the same (unless \(\displaystyle x\) happens to be \(\displaystyle 3\)). However, \(\displaystyle (x-3) = -(3 - x)\) for all \(\displaystyle x\).

 

[mmm4444bot]

"My math book says (x - 3)(x + 2) is the same as -1(3 - x)(x + 2)"

That is how it ought to appear.

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If you switch the positions of numbers in a subtraction, look what happens:

[6] - [5] = 1

[5] - [6] = -1

[10] - [-4] = 14

[-4] - [10] = -14

[-8] - [12] = -20

[12] - [-8] = 20

[-1] - [-2] = 1

[-2] - [-1] = -1

I hope this helps you "see" why (x - 3) is the same as -(3 - x). :cool:

 

[tkhunny]

My math book says (x - 3)(x + 2) is the same as -1(x - 3)(x + 2)

So if (x - 3)(x + 2) is the same as (3 - x)(x + 2).. Well I just don't get it.

I'd I substitute 6 for x in (x - 3) and (3 - x) the first one gives me 3 as an answer and the second gives me -3.

How can they both be the same?

We could have said (x-3)(x+2) = 0 and -(x-3)(x+2) = 0 have the same solution set. Zero doesn't care if you multiply it by -1.