Here you can study the following algebraic identities:
Identity I = (a + b)^{2} = a^{2} + b^{2} + 2ab
Identity II = (a + b)^{2} = a^{2} + b^{2}  2ab
Identity III = a^{2}  b^{2} = (a + b) (a  b)
Identity IV = (x + a) (x + b) = x^{2} + (a + b)x + ab
Identity V = a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca
Identity VI = (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)
How these identities are obtained and Application of these identities can be study from the above provided respective links:

