To find the sum of polynomials: \(\displaystyle{8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\) and \(\displaystyle{3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\)

Solution:

\(\displaystyle{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}\)

On simplifying further we get:

\(\displaystyle{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{8}{x}^{{3}}-{2}{x}^{{3}}-{2}{x}^{{2}}+{x}^{{2}}+{6}{x}+{x}-{2}\)

\(\displaystyle\Rightarrow{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{\left({8}{x}^{{3}}-{2}{x}^{{3}}\right)}-{\left({2}{x}^{{2}}-{x}^{{2}}\right)}+{\left({6}{x}+{x}\right)}-{2}\)

\(\displaystyle\Rightarrow{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{6}{x}^{{3}}-{x}^{{2}}+{7}{x}-{2}\)

Result:

Required expression is:

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

Solution:

\(\displaystyle{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}\)

On simplifying further we get:

\(\displaystyle{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{8}{x}^{{3}}-{2}{x}^{{3}}-{2}{x}^{{2}}+{x}^{{2}}+{6}{x}+{x}-{2}\)

\(\displaystyle\Rightarrow{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{\left({8}{x}^{{3}}-{2}{x}^{{3}}\right)}-{\left({2}{x}^{{2}}-{x}^{{2}}\right)}+{\left({6}{x}+{x}\right)}-{2}\)

\(\displaystyle\Rightarrow{\left({8}{x}^{{3}}-{2}{x}^{{2}}+{6}{x}-{2}\right)}+{\left({3}{x}^{{4}}-{2}{x}^{{3}}+{x}^{{2}}+{x}\right)}={3}{x}^{{4}}+{6}{x}^{{3}}-{x}^{{2}}+{7}{x}-{2}\)

Result:

Required expression is:

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