Factorization a3-3a2b+3ab2-b3=(a-b)3
Factorization
a3-3a2b+3ab2-b3=(a-b)3
Example 1
$$\textup{Expand } x^3-9x^2+27x-27 $$
Solution
\begin{align*}
&\because\;\;a^3-3a^2b+3ab^2-b^3=(a-b)^3\\\\
&\therefore\;\; x^3-9x^2+27x-27 \\
&=(x)^3-3(x)^2(3)+3(x)(3)^2-(3)^3\\
&=(x-3)^3\\
\end{align*}
Example 2
$$\textup{Expand } x^3-12x^2+48x-64 $$
Solution
\begin{align*}
&\because\;\;a^3-3a^2b+3ab^2-b^3=(a-b)^3\\\\
&\therefore\;\; x^3-12x^2+48x-64 \\
&=(x)^3-3(x)^2(4)+3(x)(4)^2-(4)^3\\
&=(x-4)^3\\
\end{align*}