Respuesta :
This is (x - 6)*x^1/2(x + 3)
= x^1/2 (x^2 - 3x - 18)
= x^(5/2) - 3x^(3/2) - 18x^(1/2)
= x^1/2 (x^2 - 3x - 18)
= x^(5/2) - 3x^(3/2) - 18x^(1/2)
[tex]\bf \begin{cases}
f(x)=x-6\\
g(x)=x^{\frac{1}{2}}(x+3)
\end{cases}
\\\\\\
f(x)\cdot g(x)\implies (x-6)\cdot \left[ x^{\frac{1}{2}}(x+3) \right]\implies (x-6)\cdot \left[ \stackrel{distributing}{x^{\frac{3}{2}}+3x^{\frac{1}{2}}} \right][/tex]
[tex]\bf x\left( x^{\frac{3}{2}}+3x^{\frac{1}{2}} \right)-6\left( x^{\frac{3}{2}}+3x^{\frac{1}{2}} \right) \\\\\\ x^{\frac{5}{2}}+3x^{\frac{3}{2}}~~-~~6x^{\frac{3}{2}}-18x^{\frac{1}{2}}\implies \stackrel{\textit{adding like-terms}}{x^{\frac{5}{2}}-3x^{\frac{3}{2}}-18x^{\frac{1}{2}}} \\\\\\ \stackrel{\textit{common factoring}}{x^{\frac{1}{2}}\left( x^{\frac{4}{2}}-3x^{\frac{2}{2}}-18 \right)}\implies x^{\frac{1}{2}}(x^2-3x-18)\implies x^{\frac{1}{2}}(x-6)(x+3)[/tex]
[tex]\bf x\left( x^{\frac{3}{2}}+3x^{\frac{1}{2}} \right)-6\left( x^{\frac{3}{2}}+3x^{\frac{1}{2}} \right) \\\\\\ x^{\frac{5}{2}}+3x^{\frac{3}{2}}~~-~~6x^{\frac{3}{2}}-18x^{\frac{1}{2}}\implies \stackrel{\textit{adding like-terms}}{x^{\frac{5}{2}}-3x^{\frac{3}{2}}-18x^{\frac{1}{2}}} \\\\\\ \stackrel{\textit{common factoring}}{x^{\frac{1}{2}}\left( x^{\frac{4}{2}}-3x^{\frac{2}{2}}-18 \right)}\implies x^{\frac{1}{2}}(x^2-3x-18)\implies x^{\frac{1}{2}}(x-6)(x+3)[/tex]
