The given two polynomials are, \(\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}\) and \(\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}\)

We need to subtract \(\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}\) from \(\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}\)

On combining the like terms, we simplify the given expression.

On simplifying the given expression, we get

\(\displaystyle{\left({5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}\right)}-{\left({2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}\right)}={5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}-{2}{x}^{{3}}-{x}^{{2}}+{7}{x}+{2}\)

\(\displaystyle-{\left({5}-{2}\right)}{x}^{{3}}+{\left({2}-{1}\right)}{x}^{{2}}+{\left(-{13}+{2}\right)}\)

\(\displaystyle={3}{x}^{{3}}+{x}^{{2}}-{11}\)

Therefore, the resultant expression is \(\displaystyle{3}{x}^{{3}}+{x}^{{2}}-{11}\)

We need to subtract \(\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}\) from \(\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}\)

On combining the like terms, we simplify the given expression.

On simplifying the given expression, we get

\(\displaystyle{\left({5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}\right)}-{\left({2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}\right)}={5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}-{2}{x}^{{3}}-{x}^{{2}}+{7}{x}+{2}\)

\(\displaystyle-{\left({5}-{2}\right)}{x}^{{3}}+{\left({2}-{1}\right)}{x}^{{2}}+{\left(-{13}+{2}\right)}\)

\(\displaystyle={3}{x}^{{3}}+{x}^{{2}}-{11}\)

Therefore, the resultant expression is \(\displaystyle{3}{x}^{{3}}+{x}^{{2}}-{11}\)