Exploring Algebraic Identities

An algebraic identity is true

An algebraic identity is true for all values of the variables. An equation may be true only for specific values. For example, x^2 - 1 = 24 is an equat

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

(a + b)^2 = a^2 + 2ab + b^2. It is shown using a square split into smaller parts and is also proved by the distributive property. It works for positiv

(a

(a - b)^2 = a^2 - 2ab + b^2. It is obtained by replacing b with -b in the square of sum identity.

(a + b + c)^2 =

(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca. This comes from treating b + c as one term first, then expanding again.

a^2

a^2 - b^2 = (a + b)(a - b). This identity also appears in reverse form as a shortcut for factorisation.