Consider the following algebraic identities. (i) \[{{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\] (ii) \[{{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\] (iii) \[{{a}^{2}}-{{b}^{2}}=(a-b)\,(a+b)\] (iv) \[(a+x)(a+y)={{a}^{2}}+a(x+y)+xy\] Which of the identity is/are incorrect?

• A. only (i), (ii) and (iii)
• B. only (i), (iii) and (iv)
• C. only (ii), (iii) and (iv)
• D. None of these