Simplifying problem

by **Blood Sucker** Thu Dec 07, 2017 9:03 pm

Hi fellas,
Can someone tell me why (a^2+b^2) = (a+b)^2-2ab while (a^2-b^2) = (a+b)^2-4ab
Giving that I know what does (a+b)^2 equal to.
Cheers

PS: I ain't sure about the second formula

by **Chuck Norris** Thu Dec 07, 2017 9:35 pm

Blood Sucker wrote:Hi fellas,
Can someone tell me why (a^2+b^2) = (a+b)^2-2ab while (a^2-b^2) = (a+b)^2-4ab
Giving that I know what does (a+b)^2 equal to.
Cheers

PS: I ain't sure about the second formula

1. Before the word while:
(a^2+b^2) = (a+b)^2-2ab

It's a standard formula, only written in the wrong way. Put -2ab on the other side (which changes it to +2ab) that gives you

a^2 + 2ab +b^2 = (a+b)^2

(a+b)^2 = (a+b) * (a+b) = a*a + a*b + b*a + b*b = a^2 + 2*a*b + b^2 = a^2 + 2ab + b^2.

Notes:
- If you don't know how to calculate (a+b)*(a+b), let's replace it with (a+b)*(c+d) = a*c + a*d + b*c + b*d,
- a*b is the same as b*a. You should now that, just like 2*3 is the same as 3*2.

2. After the while.

(a^2-b^2) = (a+b)^2-4ab (1)

(a+b)^2 was proven to be = a^2 + 2ab + b^2. in number 1.

Inserting it into the formula named (1), we get:
a^2 -b^2 = a^2 + 2ab + b^2 - 4ab = a^2 -2ab +b^2.

Which is wrong, since both sides can't possibly be the same.

What I think is that a^2 - b^2 is supposed to be: (a - b)^2

You can calculate that yourself like in 1 to verify it.