<PRE><B>Question 972748</B>
Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.)
{{{ (4x+5y)^6 }}} , n=4
&lt;pre&gt;&lt;font face = &quot;Tohoma&quot; size = 4 color = &quot;indigo&quot;&gt;&lt;b&gt;Use the formula for a specific term of a binomial expansion:
(a + b)&lt;sup&gt;n&lt;/sup&gt; = &lt;sub&gt;n&lt;/sub&gt;C&lt;sub&gt;(r - 1)&lt;/sub&gt; * (a)&lt;sup&gt;(n - (r - 1))&lt;/sup&gt; * (b)&lt;sup&gt;(r - 1)&lt;/sup&gt;

We have: {{{(4x + 5y)^6}}}, with:
{{{a = 4x}}}
{{{b = 5y}}}
Term number, or {{{r = 4}}}
{{{n = 6}}}
  (a + b)&lt;sup&gt;n&lt;/sup&gt;   = &lt;sub&gt;n&lt;/sub&gt;C&lt;sub&gt;(r - 1)&lt;/sub&gt; * (a)&lt;sup&gt;(n - (r - 1))&lt;/sup&gt; * (b)&lt;sup&gt;(r - 1)&lt;/sup&gt;
4&lt;sup&gt;th&lt;/sup&gt; term of: (4x + 5y)&lt;sup&gt;6&lt;/sup&gt;:   &lt;sub&gt;6&lt;/sub&gt;C&lt;sub&gt;(4 - 1)&lt;/sub&gt; * (4x)&lt;sup&gt;(6 - (4 - 1))&lt;/sup&gt; * (5y)&lt;sup&gt;(4 - 1)&lt;/sup&gt;
4&lt;sup&gt;th&lt;/sup&gt; term of (4x + 5y)&lt;sup&gt;6&lt;/sup&gt;:    &lt;sub&gt;6&lt;/sub&gt;C&lt;sub&gt;3&lt;/sub&gt; * (4x)&lt;sup&gt;3&lt;/sup&gt; * (5y)&lt;sup&gt;3&lt;/sup&gt;
4&lt;sup&gt;th&lt;/sup&gt; term of (4x + 5y)&lt;sup&gt;6&lt;/sup&gt;:    20 * 64x&lt;sup&gt;3&lt;/sup&gt; * 125y&lt;sup&gt;3&lt;/sup&gt;
4&lt;sup&gt;th&lt;/sup&gt; term of {{{(4x + 5y)^6}}}:   {{{highlight_green(160000x^3y^3)}}}&lt;/font face = &quot;Tohoma&quot; size = 4 color = &quot;indigo&quot;&gt;&lt;/b&gt;</PRE>