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

Rivka Thorpe 2021-09-16 Answered
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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Expert Answer

lamanocornudaW
Answered 2021-09-17 Author has 3652 answers
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, \(\displaystyle{3}{\left({x}^{{2}}\right)}{\left({5}{x}\right)}{\left(-{\frac{{{2}}}{{{3}}}}{x}^{{3}}\right)}=-{10}{x}^{{6}}\)
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