Question

can we write a^2+b^2=(a+b)^2​

Answer 1

It's wrong...

Correct formula is

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

Answer 2

No.

$LHS:a^2+b^2\\RHS:(a+b)^2\\=a^2+b^2+2ab$

Hence, we can see that LHS ≠ RHS.

Additional:

If we take RHS as $(a+b)^2-2ab$  then we can say that both are equal.