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*}