$${\left(\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}\right)}^{{\mathtt{4}}}$$
how to expand it
((1/2)x-3)^4
$$=\left(\frac{x}{2}-3\right)^4=\left(\frac{x-6}{2}\right)^4=\frac{1}{16}(x-6)^4$$
$$=\frac{1}{16}
( \
\textcolor[rgb]{1,0,0}{1} *x^{\textcolor[rgb]{0,1,0}{4}}*6^{\textcolor[rgb]{0,0,1}{0}}
-\textcolor[rgb]{1,0,0}{4} *x^{\textcolor[rgb]{0,1,0}{3}}*6^{\textcolor[rgb]{0,0,1}{1}}
+\textcolor[rgb]{1,0,0}{6} *x^{\textcolor[rgb]{0,1,0}{2}}*6^{\textcolor[rgb]{0,0,1}{2}}
-\textcolor[rgb]{1,0,0}{4} *x^{\textcolor[rgb]{0,1,0}{1}}*6^{\textcolor[rgb]{0,0,1}{3}}
+\textcolor[rgb]{1,0,0}{1} *x^{\textcolor[rgb]{0,1,0}{0}}*6^{\textcolor[rgb]{0,0,1}{4}}
\ )$$ $$\left[ \small{\text{Pascal 4: 1,4,6,4,1}} \right]$$
$$=\frac{1}{16}
(\
x^4-4*x^3*6+6*x^2*6^2-4*x*6^3+6^4
\ )$$
$$=\frac{1}{16}
( \
x^4-24x^3+216x^2-864x+1296
\ )$$
$$=
\frac{1}{16}x^4
-\frac{3}{2} x^3
+\frac{27}{2}x^2
-54x
+81$$
((1/2)x-3)^4
$$=\left(\frac{x}{2}-3\right)^4=\left(\frac{x-6}{2}\right)^4=\frac{1}{16}(x-6)^4$$
$$=\frac{1}{16}
( \
\textcolor[rgb]{1,0,0}{1} *x^{\textcolor[rgb]{0,1,0}{4}}*6^{\textcolor[rgb]{0,0,1}{0}}
-\textcolor[rgb]{1,0,0}{4} *x^{\textcolor[rgb]{0,1,0}{3}}*6^{\textcolor[rgb]{0,0,1}{1}}
+\textcolor[rgb]{1,0,0}{6} *x^{\textcolor[rgb]{0,1,0}{2}}*6^{\textcolor[rgb]{0,0,1}{2}}
-\textcolor[rgb]{1,0,0}{4} *x^{\textcolor[rgb]{0,1,0}{1}}*6^{\textcolor[rgb]{0,0,1}{3}}
+\textcolor[rgb]{1,0,0}{1} *x^{\textcolor[rgb]{0,1,0}{0}}*6^{\textcolor[rgb]{0,0,1}{4}}
\ )$$ $$\left[ \small{\text{Pascal 4: 1,4,6,4,1}} \right]$$
$$=\frac{1}{16}
(\
x^4-4*x^3*6+6*x^2*6^2-4*x*6^3+6^4
\ )$$
$$=\frac{1}{16}
( \
x^4-24x^3+216x^2-864x+1296
\ )$$
$$=
\frac{1}{16}x^4
-\frac{3}{2} x^3
+\frac{27}{2}x^2
-54x
+81$$