What is the Expanded Formula for a Square?

[MathematicalPhysicist]

[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)]
the book expands it to:
(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

i didnt get it so can someone please help me in this, i think there is a mistake in the book.

 

[KLscilevothma]

Originally posted by loop quantum gravity
[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)]
the book expands it to:
(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)] does not equal to(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

However,
[(x3-x2)+(x2-x1)]*[(x3-x2)+(x2-x1)] = (x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

 

[MathematicalPhysicist]

Originally posted by KL Kam
[(x3-x2)+(x2-x1)]*[(x3+x2)+(x2-x1)] does not equal to(x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

However,
[(x3-x2)+(x2-x1)]*[(x3-x2)+(x2-x1)] = (x3-x2)^2+2(x3-x2)*(x2-x1)+(x2-x1)^2

have you noticed the experssions on the right are the same?

 

[KLscilevothma]

Please read the expressions on the left hand sides carefully. I changed a "+" sign to a "-" sign in the third small bracket

 

[MathematicalPhysicist]

yes you are right. i guess it was a type mistake )-:

 

[HallsofIvy]

With the negative, it is simply the formula for a square:

(a+b)*(a+b)= a²+ 2ab+ b²

with a= x₃-x₂ and b= x₂- x₁