Step 1

Let us consider the given algebraic expression and can be factorize as shown.

\(\displaystyle{5}{x}^{{{3}}}{y}-{15}{x}^{{{2}}}{y}+{10}{x}{y}\)

\(\displaystyle={5}{x}{y}{\left({x}^{{{2}}}-{3}{x}+{2}\right)}\)

\(\displaystyle={5}{x}{y}{\left({x}^{{{2}}}-{2}{x}-{x}+{2}\right)}\)

\(\displaystyle={5}{x}{y}({x}{\left({x}-{2}\right)}-{\left({x}-{2}\right)})\)

\(\displaystyle={5}{x}{y}{\left({x}-{2}\right)}{\left({x}-{1}\right)}\)