<PRE><B>Question 24457</B>
&lt;pre&gt;Express as a polynomial 
(2x+10y)^3
&lt;b&gt;&lt;font size = 4&gt;
(2x + 10y)&lt;sup&gt;3&lt;/sup&gt;

This can be done by the binomial theorem.  If that is the
way you were told to do it, post again.  I will only show 
you the basic method, which gives the same answer.

Write the cube as multiplication three times

(2x + 10y)(2x + 10y)(2x + 10y)

Use FOIL to multiply out the second and third parentheses:

(2x + 10y)(4x&lt;sup&gt;2&lt;/sup&gt; + 20xy + 20xy + 100y&lt;sup&gt;2&lt;/sup&gt;)

Collect terms in the second parentheses

(2x + 10y)(4x&lt;sup&gt;2&lt;/sup&gt; + 40xy + 100y&lt;sup&gt;2&lt;/sup&gt;)

Use the distributive principle to multiply the two terms
in the first parentheses by the trinomial in the second 
parentheses.

2x(4x&lt;sup&gt;2&lt;/sup&gt; + 40xy + 100y&lt;sup&gt;2&lt;/sup&gt;) + 10y(4x&lt;sup&gt;2&lt;/sup&gt; + 40xy + 100y&lt;sup&gt;2&lt;/sup&gt;)

then distribute each:

   8x&lt;sup&gt;3&lt;/sup&gt; + 80x&lt;sup&gt;2&lt;/sup&gt;y + 200xy&lt;sup&gt;2&lt;/sup&gt; + 40x&lt;sup&gt;2&lt;/sup&gt;y + 400xy&lt;sup&gt;2&lt;/sup&gt; + 1000y&lt;sup&gt;3&lt;/sup&gt;

Collect like terms:

  8x&lt;sup&gt;3&lt;/sup&gt; + 120x&lt;sup&gt;2&lt;/sup&gt;y + 600xy&lt;sup&gt;2&lt;/sup&gt; + 1000y&lt;sup&gt;3&lt;/sup&gt;

Edwin
AnlytcPhil@aol.com&lt;/pre&gt;


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