# To factorize: 5x^{3}y-15x^{2}y+10xy

To factorize:
$$\displaystyle{5}{x}^{{{3}}}{y}-{15}{x}^{{{2}}}{y}+{10}{x}{y}$$

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Step 1
Let us consider the given algebraic expression and can be factorize as shown.
$$\displaystyle{5}{x}^{{{3}}}{y}-{15}{x}^{{{2}}}{y}+{10}{x}{y}$$
$$\displaystyle={5}{x}{y}{\left({x}^{{{2}}}-{3}{x}+{2}\right)}$$
$$\displaystyle={5}{x}{y}{\left({x}^{{{2}}}-{2}{x}-{x}+{2}\right)}$$
$$\displaystyle={5}{x}{y}({x}{\left({x}-{2}\right)}-{\left({x}-{2}\right)})$$
$$\displaystyle={5}{x}{y}{\left({x}-{2}\right)}{\left({x}-{1}\right)}$$