a, \(m^3+27\)
\(\Leftrightarrow m^3+3^3\)
\(\Leftrightarrow\left(m+3\right)\left(m^2-m.3+3^2\right)\)
\(\Leftrightarrow\left(m+3\right)\left(m^2-3m+9\right)\)
b,\(\frac{1}{27}+a^3\)
\(\Leftrightarrow\frac{1}{27}\left(1+27a^3\right)\)
\(\Leftrightarrow\frac{1}{27}.\left(1+3a\right)\left(1-3a+9a^2\right)\)
c,\(\left(a+b\right)^3-c^3\)
\(\Leftrightarrow\left(a+b-c\right)\left[\left(a+b\right)^2+\left(a+b\right)c+c^2\right]\)
\(\Leftrightarrow\left(a+b-c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)
d,\(x^9+1\)
\(\Leftrightarrow\left(x^3+1\right)\left(x^6-x^3+1\right)\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x+1\right)\left(x^6-x^3+1\right)\)
e,\(x^3+9x^2+27x+27\)
\(\Leftrightarrow x^3+3.x^2.3+3x.9+3^3\)
\(\Leftrightarrow x^3+3x^2.3+3x+3^2+3^3\)
\(\Leftrightarrow\left(x+3\right)^3\)
