Basic Algebraic Identities

Class 9: One shot Basic Algebraic Identities for quick revision at exam time.

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

\((a-b)^2 = a^2 – 2ab + b^2\)

\(
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
\)

\(
(a+b)^3 = a^3 + b^3 + 3ab(a+b)
\)

\(
(a-b)^3 = a^3 – 3a^2b + 3ab^2 – b^3
\)

\(
(a-b)^3 = a^3 – b^3 – 3ab(a-b)
\)

\(
a^3 + b^3 = (a+b)(a^2 – ab + b^2)
\)

\(
a^3 – b^3 = (a-b)(a^2 + ab + b^2)
\)

\(
(a+b)(a-b) = a^2 – b^2
\)

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

\(a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
\)

\(a^3 + b^3 + c^3 – 3abc = \)

\( (a+b+c)(a^2 + b^2 + c^2 – ab – bc – ca)\)

\(\text{If } a+b+c = 0,\) \(\text{ then } a^3 + b^3 + c^3 = 3abc.\)