  Yulia 2021-09-18 Answered
$$\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}$$

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A polynomial in a variable x is a function of the form $$\displaystyle{a}_{{n}}{x}^{{n}}+{a}_{{{n}-{1}}}{x}^{{{n}-{1}}}+\ldots+{a}_{{1}}{x}+{a}_{{0}}$$. This polynomial has degree n. The constants $$\displaystyle{a}_{{i}}$$ are the coefficients and are constants.
To add two polynomials we add like terms, that is, add terms of the same degree. For example $$\displaystyle{2}{x}^{{2}},{4}{x}^{{2}}$$ are terms of the same degree but the terms $$\displaystyle{2}{x}^{{2}},{4}{x}^{{3}}$$ are terms of different degree.
The sum to be computed is $$\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}$$. . Drop the parenthesis and combine like terms.
$$\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}={7}{x}^{{2}}-{6}{x}+{3}{x}^{{3}}-{9}{x}$$
$$\displaystyle={3}{x}^{{3}}+{7}{x}^{{2}}+{\left(-{6}{x}-{9}{x}\right)}+{6}$$
$$\displaystyle={3}{x}^{{3}}+{7}{x}^{{2}}-{15}{x}+{6}$$
Hence, the sum is $$\displaystyle{3}{x}^{{3}}+{7}{x}^{{2}}-{15}{x}+{6}$$.