We know \((a + b)^2 = a^2 + 2ab + b^2\).
What if we want the square of the sum of three numbers \(a\), \(b\) and \(c\)?
\((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\)
Some More Identities:
\(a^2 - b^2 = (a + b)(a - b)\)
\((a + b)^3 = a^3 + 3ab^2 + 3a^2b + b^3 = a^3 + 3ab(a + b) + b^3\)
\((a - b)^3 = a^3 + 3ab^2 - 3a^2b - b^3 = a^3 - 3ab(a - b) - b^3\)
\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)
\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\)