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## Standard Identities & their applications

(a + b)^{2} = a^{2} + b^{2} + 2ab (a - b)^{2} = a^{2} + b^{2} - 2ab a^{2} - b^{2} = (a + b) (a - b) (x + a) (x + b) = x^{2} + x(a + b) + ab (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca (a + b)^{3} = a^{3} + b^{3} + 3ab(a + b) (a - b)^{3} = a^{3} - b^{3} - 3ab(a - b) a^{3} + b^{3} + c^{3} - 3abc = (a + b + c)(a^{2} + b^{2} + c^{2} - ab - bc - ca)

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: