# Show that (2a-1)^2 - (2b-1)^2 = 4(a-b)(a+b-1)

1. Mar 7, 2007

### Trail_Builder

hope you can help, thnx

1. The problem statement, all variables and given/known data

Show that (2a-1)^2 - (2b-1)^2 = 4(a-b)(a+b-1)

2. Relevant equations

n/a

3. The attempt at a solution

I thought that i needed to rearrange (2a-1)^2 - (2b-1)^2 to show 4(a-b)(a+b-1)

my attempt...

4a^2 - 4a + 1 - 4b^2 - 4b + 1
4(a^2 - a + (1/4) - b^2 - b + (1/4))
4(a^2 - a - b^2 - b + (1/2))

then i turnt that to this which i really think is going the wrong direction lol

4(a(a-1)-b(b+1)+(1/2))

lol

anyways, if i was to try and solve my errors myself id tell myself to try and extract the (a-b) as a factor from 4(a^2 - a + (1/4) - b^2 - b + (1/4))

hope you can help

thnx

2. Mar 7, 2007

### dontdisturbmycircles

4a^2 - 4a + 1 - 4b^2 - 4b + 1

Can you see the mistake? Use brackets to expand (2a-1)^2 - (2b-1)^2! :)

Tell me if you need more help, I will be glad to help. (or if I am offline, someone else will)

Last edited: Mar 7, 2007
3. Mar 7, 2007

### dontdisturbmycircles

note that a - [b - a] = a -b + a = 2a-b

After you figure that part out, just expand this : 4(a-b)(a+b-1) and you will see similarities between what you have and what they want .

4. Mar 7, 2007

### Trail_Builder

i may be wrong, but is (2a-1)^2 - (2b-1)^2

4a^2 - 4a + 1 - 4b^2 + 4b - 1 ???

thnx for the help

5. Mar 7, 2007

### dontdisturbmycircles

Yes, you are correct there.

So now simplify it to $$4a^{2} - 4a -4b^{2}+4b$$

Now what is 4(a-b)(a+b-1) once you expand it.

Last edited: Mar 7, 2007
6. Mar 7, 2007

### Trail_Builder

o rite sweet, i got it :D

thnx buddy for the help