Algebraic Identity (a+b)3=a3+3a2b+3ab2+b3
Algebraic Identity
(a+b)3=a3+3a2b+3ab2+b3
Example 1
$$\textup{Expand } (x+3)^3 $$
Solution
\begin{align*}
\because\;\;(a+b)^3&=a^3+3a^2b+3ab^2+b^3\\\\
\therefore\;\; (x+3)^3&=(x)^3+3(x)^2(3)+3(x)(3)^2+(3)^3\\
&=x^3+3(x^2)(3)+3(x)(9)+27\\
&=x^3+9x^2+27x+27\\
\end{align*}
Example 2
$$\textup{Expand } (x+5)^3 $$
Solution
\begin{align*}
\because\;\;(a+b)^3&=a^3+3a^2b+3ab^2+b^3\\\\
\therefore\;\; (x+5)^3&=(x)^3+3(x)^2(5)+3(x)(5)^2+(5)^3\\
&=x^3+3(x^2)(5)+3(x)(25)+125\\
&=x^3+15x^2+75x+125\\
\end{align*}