Algebra: How does [-x^2 -4x+4-1] become [(x^2+4x-4)-1]

1. Aug 31, 2013

LearninDaMath

If I want to complete the square with

$(-x^{2}-4x+3)$ I would write

$(-x^{2}-4x+(...) +3 - (...)) = (-x^{2}-4x+4+3-4) = (-x^{2}-4x+4-1) = (x^{2}+4x-4) - 1$

Why does adding the parentheses to separate the -1 change all the signs. I understand it has something to do with factoring out a negative, but how exactly?

I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the -1 when completing the square for an integration problem in calculus?

Last edited: Aug 31, 2013
2. Aug 31, 2013

arildno

"I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the -1 when completing the square for an integration problem in calculus? "

It doesn't; you are perfectly correct concerning addition/subtraction relative to the associative property.

The last expression is missing a minus sign in front of the parenthesis expression containing the completed square.

3. Aug 31, 2013

NextElement

-(x^2+4x-4)+7 ?

4. Sep 1, 2013

verty

There's a mistake, x^2 + 4x - 4 is not a square.

The correct way to start is:

-x^2 - 4x + 3
-(x^2 + 4x) + 3

5. Sep 1, 2013

NextElement

I'm confused as heck, but this is good practice since this is exactly what we're reviewing in math right now.

If you start with -(x^2+4x) + 3, you divide that 4 by two and square it, resulting in -(x^2+4x+4)+3.

However, you have do add that 4 to the outside, but doesn't the negative in the very front make it a negative 4, finally resulting in -(x^2+4x+4) + 7? I'm confused on where to go from here.

6. Sep 2, 2013

verty

You have done the hard work, you just need to write it in the neatest way possible. Remember you want to have something like (x+a)^2.

Here is a more abstract example for you to practice the steps on:

x^2 + px + q = 0

7. Sep 2, 2013

NextElement

Think I got it:

-(x+2)^2 + 7? :)