(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the term with the specified power in the expansion of the given binomial power.

[tex]

\left( {x^3 + y^2 } \right)^{42} ,\,\,\,\,\,y^{15}

[/tex]

2. Relevant equations

[tex]{\rm{term}} = \frac{{n!}}{{r!\left( {n - r} \right)!}}x^{n - r} y^r [/tex]

3. The attempt at a solution

[tex]\begin{array}{l}

{\rm{term}} = \frac{{42!}}{{15!\left( {42 - 15} \right)!}}x^{3 \cdot \left( {42 - 15} \right)} y^{2 \cdot 15} \\

\\

{\rm{term}} = \frac{{42!}}{{15!\left( {27} \right)!}}x^{81} y^{30} \\

{\rm{term}} = {\rm{98672427616}}\,x^{81} y^{30} \\

\end{array}

[/tex]

The back of the book says no such term exists. Why? Is it because x has an exponent that is higher than n? x^3 doesn't have a higher exponent, and I thought that's all that mattered.

Also, is there a way of simplifying that factorial so I don't have to rely completely on the calculator to solve? Thanks!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Binomial formula

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