Question

Discuss possible conditions on a and b that would make this a valid equation: (a-b)^2 does not equal a^2-b^2.

Answer 1

First of all, evaluate (a-b)^2.

Answer 2

a^2-2ab+b^2

Answer 3

Okay now if we say:
a^2-b^2 = a^2-2ab+b^2

Subtract a^2 and get:
-b^2 = -2ab+b^2
Subtract b^2 and get:
-2b^2 = -2ab
Divide by -2
b^2 = ab
Divide by b:
a=b

Answer 4

So we have two cases, a=b and b=0, where they are equal.
If this isn't true, then (a-b)^2 does not equal a^2-b^2.