30 points for this !how can polynomial identities be proven?

They are generally proven by carrying out the indicated operations and/or regrouping. When multiple polynomials or specific conditions are involved, substitution may also be part of the proof.

Start with the un-simplified side, (x+y)2
The expression (x+y)2 can be re-written as (x+y)(x+y). 
The expression (x+y)(x+y) can be multiplied using the Distributive Property. That results in x2+xy+xy+y2. 
The expression x2+xy+xy+y2 can be simplified by adding the middle terms. This results in x2+2xy+y2. 
This proves that (x+y)2 = x2+2xy+y2. 

I hope this helps clear things up! 

It’s 8.99 for john hub b