This tests helped me find many bugs in my programm.
a + b
a + b
---
a^2 + 2*a*b + b^2

a + b
a - b
---
a^2 - b^2

a - b
a - b
---
a^2 - 2*a*b + b^2

And this:
12*x + 15*x^2 - 21y^1*y
5*a^1 - 1 + 0 + 1*b*b*b
---
15*b^3*x^2 - 21*b^3*y^2 + 12*b^3*x + 75*a*x^2 - 105*a*y^2 + 60*a*x - 15*x^2 + 21*y^2 - 12*x

Last test is very useful. Thx. But there is a bug in the first line :  21y^1*y - multipliers must be separated with '*' symbols

Oh, yes! Of course you are right. Sorry for my mistake.

There can be whitespaces in the beginning of the expression