Step 1

Concept used:

The multiplication of the expression \(\displaystyle{\left({8}{x}-{3}\right)}{\left({2}{x}-{4}\right)}\) is calculated as,

\(\displaystyle{\left({8}{x}-{3}\right)}{\left({2}{x}-{4}\right)}={8}{x}{\left({2}{x}-{4}\right)}-{3}{\left({2}{x}-{4}\right)}\)

\(\displaystyle={\left({8}{x}\right)}\cdot{\left({2}{x}\right)}+{\left({8}{x}\right)}\cdot{\left(-{4}\right)}+{\left(-{3}\right)}\cdot{\left({2}{x}\right)}+{\left(-{3}\right)}\cdot{\left(-{4}\right)}\)

\(\displaystyle={16}{x}^{{{2}}}-{32}{x}-{6}{x}+{12}\)

\(\displaystyle={16}{x}^{{{2}}}-{38}{x}+{12}\)

Thus, the multiplication of the expression \(\displaystyle{\left({8}{x}-{3}\right)}{\left({2}{x}-{4}\right)}\) is \(16x^{2}-38x+12\)