\begin{equation*}
\begin{split}
x^3\: – \:27& = x^3 \:-\: 3^3\\\\
x^3\: – \:27& = (x\:-\:3)(x^2 + x\cdot 3 + 3^2)\\\\
x^3\: – \:27& = (x\:-\: 3)(x^2 + 3x + 9)
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
x^3 + 64& = x^3 + 4^3\\\\
x^3 + 64& = (x + 4)(x^2\: – \:x\cdot 4 + 4^2)\\\\
x^3 + 64& = (x+ 4)(x^2 \:- \:4x + 16)
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
1 \: – \:8x^3& = 1^3\: – \:2^3x^3\\\\
1 \: – \:8x^3& = 1^3 \:-\: (2x)^3\\\\
1 \: – \:8x^3& = (1\:-\:2x)(1^2 + 1\cdot 2x + (2x)^2)\\\\
1 \: – \:8x^3& = (1\:-\:2x)(1 + 2x + 4x^2)
\end{split}
\end{equation*}
[/su_table]
\begin{equation*}
\begin{split}
125x^3 + \dfrac{1}{8}y^3& = 5^3x^3 + \left(\dfrac{1}{2}\right)^3y^3\\\\
125x^3 + \dfrac{1}{8}y^3& = (5x)^3 + \left(\dfrac{1}{2}y\right)^3\\\\
125x^3 + \dfrac{1}{8}y^3& = (5x + \dfrac{1}{2}y)\left[(5x)^2 \:-\: 5x\cdot \dfrac{1}{2}y + \left(\dfrac{1}{2}y\right)^2\right]\\\\
125x^3 + \dfrac{1}{8}y^3& = (5x + \dfrac{1}{2}y)\left(25x^2\: -\: \dfrac{5}{2}xy + \dfrac{1}{4}y^2\right)
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
x^6 \:- \:y^6& = (x^2)^3 \:-\: (y^2)^3\\\\
x^6 \:- \:y^6& = (x^2\: – \:y^2)[(x^2)^2 + x^2y^2 + (y^2)^2]\\\\
x^6 \:- \:y^6& = (x+y)(x\:-\:y)(x^4 + x^2y^2 + y^4)
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
40m^3n + 135n& = 5n(8m^3 + 27)\\\\
40m^3n + 135n& = 5n[(2m)^3 + 3^3]\\\\
40m^3n + 135n& = 5n(2m + 3)[(2m)^2\: – \:2m\cdot 3 + 3^2]\\\\
40m^3n + 135n& = 5n(2m + 3)(4m^2 \:- \: 6m + 9)
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
(2m + 5)(4m^2\: – \:10m + 25)& = (2m + 5)[(2m)^2 \:- \:2m\cdot 5 + 5^2]\\\\
(2m + 5)(4m^2\: – \:10m + 25)& = (2m)^3 + 5^3\\\\
(2m + 5)(4m^2\: – \:10m + 25)& = 8m^3 + 125
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
(x\:-\:3y)(x^2 + 3xy + 9y^2)& = (x\:-\:3y)(x^2 + x\cdot 3y +(3y)^2)\\\\
(x\:-\:3y)(x^2 + 3xy + 9y^2)& = x^3\: – \:(3y)^3\\\\
(x\:-\:3y)(x^2 + 3xy + 9y^2)& = x^3\:-\:27y^3
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
(1\: – \:5mn)(1 + 5mn + 25m^2n^2)& = (1 \: – \: 5mn)[1 + 1\cdot 5mn + (5mn)^2]\\\\\
(1\: – \:5mn)(1 + 5mn + 25m^2n^2)& = 1^3 \: – \: (5mn)^3\\\\\
(1\: – \:5mn)(1 + 5mn + 25m^2n^2)& = 1\: – \:125m^3n^3
\end{split}
\end{equation*}
Jabarkan \((x^{\frac{1}{3}} + y^{\frac{1}{3}})(x^{\frac{2}{3}} \:-\: x^{\frac{1}{3}}x^{\frac{1}{3}}+ y^{\frac{2}{3}})\)
\begin{equation*}
\begin{split}
& (x^{\frac{1}{3}} + y^{\frac{1}{3}})[(x^{\frac{1}{3}})^2 \:- \:x^{\frac{1}{3}}\cdot y^{\frac{1}{3}}+ (y^{\frac{1}{3}})^2]\\\\
&(x^{\frac{1}{3}})^3 + (y^{\frac{1}{3}})^3\:\:\:\:\:\color{blue} (a^m)^n = a^{m\times n}\\\\
&x + y
\end{split}
\end{equation*}
