Given polynomial are \(\displaystyle{\left({2}{a}^{{3}}{b}\right)}\) and \(\displaystyle{\left({4}{a}^{{3}}{b}+{2}\right)}\)

On adding these two polynomials, resultant polynomial is

\(\displaystyle{\left({2}{a}^{{3}}{b}+{1}\right)}+{\left({4}{a}^{{3}}{b}+{2}\right)}\)

\(\displaystyle={\left({2}{a}^{{3}}{b}+{4}{a}^{{3}}{b}\right)}+{3}\)

\(\displaystyle={6}{a}^{{3}}{b}+{3}\)

So, resultant polynomial is \(\displaystyle{6}{a}^{{3}}{b}+{3}\)

On adding these two polynomials, resultant polynomial is

\(\displaystyle{\left({2}{a}^{{3}}{b}+{1}\right)}+{\left({4}{a}^{{3}}{b}+{2}\right)}\)

\(\displaystyle={\left({2}{a}^{{3}}{b}+{4}{a}^{{3}}{b}\right)}+{3}\)

\(\displaystyle={6}{a}^{{3}}{b}+{3}\)

So, resultant polynomial is \(\displaystyle{6}{a}^{{3}}{b}+{3}\)