$$\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}=$$

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Example:
$$\displaystyle{\left({x}+{2}\right)}+{\left({x}^{{2}}+{3}{x}+{4}\right)}={x}+{2}+{x}^{{2}}+{3}{x}+{4}$$
$$\displaystyle={x}^{{2}}+{3}{x}+{x}+{2}+{4}$$
$$\displaystyle={x}^{{2}}+{4}{x}+{6}$$
Here we have combined the terms x with x and constants with constants.
Applying addition property of the polynomial for the given expression, we get
$$\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={3}{x}^{{2}}+{2}{x}+{4}+{8}{x}^{{2}}-{x}+{1}$$
$$\displaystyle={3}{x}^{{2}}+{8}{x}^{{2}}+{2}{x}-{x}+{4}+{1}$$
$$\displaystyle={11}{x}^{{2}}+{x}+{5}$$
Hence, we can fill in the blanks:
$$\displaystyle{\left({3}{x}^{{2}}+{2}{x}+{4}\right)}+{\left({8}{x}^{{2}}-{x}+{1}\right)}={11}{x}^{{2}}+{x}+{5}$$