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

[Trail_Builder]

hope you can help, thnx

Homework Statement

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

Homework Equations

n/a

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

 

[dontdisturbmycircles]

Look at your first step.

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)

 

[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 .

 

[Trail_Builder]

Look at your first step.

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)

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

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

thnx for the help

 

[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.

 

[Trail_Builder]

o rite sweet, i got it :D

thnx buddy for the help