Identities — Chapter Summary

An identity is an algebraic equation

An identity is an algebraic equation wherein both the sides give the same result for every value of the variable(s) used in it. For example, (a + 2)(a

Special products are multiplications of certain

Special products are multiplications of certain types of expressions obtained by direct or short-cut method. The four main forms are: (x + a)(x + b) =

The identity (x + y)(x

The identity (x + y)(x - y) = x^2 - y^2 gives the difference of squares. It also works in reverse: x^2 - y^2 = (x + y)(x - y).

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

(a + b)^2 = a^2 + b^2 + 2ab and (a - b)^2 = a^2 + b^2 - 2ab. The square of a sum adds the cross term, while the square of a difference subtracts it.

(a + b + c)^2 =

(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca). Also, (a + b - c)^2 = a^2 + b^2 + c^2 + 2ab - 2bc - 2ca = a^2 + b^2 + c^2 + 2(ab - bc - ca).