Algebraic Identity (a-b)(a2+ab+b2)=a3-b3
Algebraic Identity
(a-b)(a2+ab+b2)=a3-b3
Example 1
$$\textup{Expand } (x-3)(x^2+3x+9)$$
Solution
\begin{align*}
\because\;\;&(a-b)(a^2+ab+b^2)=a^3-b^3\\\\
\therefore\;\; &(x-3)(x^2+3x+9)\\
&=(x-3)[(x)^2+(x)(3)+(3)^2]\\
&=(x)^3-(3)^3\\
&=x^3-27\\
\end{align*}
Example 2
$$\textup{Expand } (c-2)(c^2+2c+4)$$
Solution
\begin{align*}
\because\;\;&(a-b)(a^2+ab+b^2)=a^3-b^3\\\\
\therefore\;\; &(c-2)(c^2+2c+4)\\
&=(c-2)[(c)^2+(2)(2)+(2)^2]\\
&=(c)^3-(2)^3\\
&=c^3-8\\
\end{align*}