# If the directions is to simplify the following polynomials, then explain what I perhaps did wrong or explain what the answer should be.

If the directions is to simplify the following polynomials, then explain what I perhaps did wrong or explain what the answer should be.
$$\displaystyle{3}{x}^{{2}}{\left({5}{x}\right)}{\left(-{\frac{{{2}}}{{{3}}}}{x}^{{3}}\right)}\to{15}{x}^{{3}}-{2}{x}^{{5}}$$

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lamanocornudaW
To solve the polynomial $$\displaystyle{3}{x}^{{2}}{\left({5}{x}\right)}{\left(-{\frac{{{2}}}{{{3}}}}{x}^{{3}}\right)}$$
Apply the rule: $$\displaystyle{a}{\left(-{b}\right)}=-{a}{b}$$
$$\displaystyle{3}{\left({x}^{{2}}\right)}{\left({5}{x}\right)}{\left(-{\frac{{{2}}}{{{3}}}}{x}^{{3}}=-{\left({3}{x}^{{2}}\right)}{\left({5}{x}\right)}{\left({\frac{{{2}}}{{{3}}}}{x}^{{3}}\right)}\ {\left({a}{\left(-{b}\right)}=-{a}{b}\right)}\right.}$$
$$\displaystyle=-{3}{x}^{{{2}+{1}+{3}}}{\left({5}\right)}{\left({\frac{{{2}}}{{{3}}}}\right)}\ {\left({a}^{{b}}.{a}^{{c}}={a}^{{{b}+{c}}}\right)}$$
$$\displaystyle=-{3}{x}^{{6}}\cdot{5}\cdot{\frac{{{2}}}{{{3}}}}$$
$$\displaystyle=-{10}{x}^{{6}}$$
Therefore, $$\displaystyle{3}{\left({x}^{{2}}\right)}{\left({5}{x}\right)}{\left(-{\frac{{{2}}}{{{3}}}}{x}^{{3}}\right)}=-{10}{x}^{{6}}$$