Question

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

Answer 1

bb

Explanation:

Answer 2

`\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((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((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`