Given Expression to simplify is

\(\displaystyle{\left({x}^{{3}}-{x}^{{2}}-{2}{x}\right)}-{\left(-{11}{x}^{{4}}-{9}{x}-{6}\right)}\)

We need to subtrax the polynomials.

Formula used:

\(\displaystyle-{\left(-{a}\right)}={a}\)

On simplifying using the expansion of brackets,

\(\displaystyle{x}^{{3}}-{x}^{{2}}-{2}{x}+{11}{x}^{{4}}+{9}{x}+{6}\)

\(\displaystyle\Rightarrow{11}{x}^{{4}}+{x}^{{3}}-{x}^{{2}}-{2}{x}+{9}{x}+{6}\)

\(\displaystyle{11}{x}^{{4}}+{x}^{{3}}-{x}^{{2}}+{7}{x}+{6}\)

The above expression is the answer we get after subtraction.

\(\displaystyle{\left({x}^{{3}}-{x}^{{2}}-{2}{x}\right)}-{\left(-{11}{x}^{{4}}-{9}{x}-{6}\right)}\)

We need to subtrax the polynomials.

Formula used:

\(\displaystyle-{\left(-{a}\right)}={a}\)

On simplifying using the expansion of brackets,

\(\displaystyle{x}^{{3}}-{x}^{{2}}-{2}{x}+{11}{x}^{{4}}+{9}{x}+{6}\)

\(\displaystyle\Rightarrow{11}{x}^{{4}}+{x}^{{3}}-{x}^{{2}}-{2}{x}+{9}{x}+{6}\)

\(\displaystyle{11}{x}^{{4}}+{x}^{{3}}-{x}^{{2}}+{7}{x}+{6}\)

The above expression is the answer we get after subtraction.