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mixas84 [53]
3 years ago
9

Which expression represents the sixth term in the binomial expansion of (5y+3)^10

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
8 0
\bf \textit{the coefficient and values of an expanded term}\\\\
(5y-3)^{10} \qquad \qquad 
\begin{array}{llll}
expansion\\
for\\
6^{th}~term
\end{array} \quad 
\begin{cases}
\stackrel{term}{k}=0..10\\
\stackrel{exponent}{10}\\
-----\\
k=\stackrel{6^{th}~term}{5}\\
n=10
\end{cases}

\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}

\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)}
\\\\\\
252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243)
\\\\\\
-191362500y^5
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