Factorization a3-b3=(a-b)(a2+ab+b2)
Factorization
a3-b3=(a-b)(a2+ab+b2)
Example 1
$$\textup{Expand } 8x^3-27 $$
Solution
\begin{align*}
\because\;\;& a^3-b^3=(a-b)(a^2+ab+b^2)\\\\
&\therefore\;\; 8x^3-27\\
&=(2x)^3-(3)^3\\
&=(2x-3)[(2x)^2+(2x)(3)+(3)^2]\\
&=(2x-3)(4x^2+6x+9)\\
\end{align*}
Example 2
$$\textup{Expand } 27x^3-64 $$
Solution
\begin{align*}
\because\;\;& a^3-b^3=(a-b)(a^2+ab+b^2)\\\\
&\therefore\;\; 27x^3-64\\
&=(3x)^3-(4)^3\\
&=(3x-4)[(3x)^2+(3x)(4)+(4)^2]\\
&=(3x-4)(9x^2+12x+16)\\
\end{align*}