<PRE><B>Question 698243</B>
&lt;pre&gt;
(2x-3)&lt;sup&gt;4&lt;/sup&gt;

Here&#39;s how to do it, and the principle works for all cases of (A+B)&lt;sup&gt;N&lt;/sup&gt;.
I&#39;ll go through every step in great detail.  But you will learn to shorten
the process by combining steps and doing some of the easy parts in your head:

The power is 4. 1 more than 4 is five, so write (2x) (-3) five times
with + signs between

 (2x) (-3)  +  (2x) (-3)  +  (2x) (-3)  +  (2x) (-3)  +  (2x) (-3) 


From left to right put the exponents 4,3,2,1,0 on the (2x)&#39;s

 (2x)&lt;sup&gt;4&lt;/sup&gt;(-3)  +  (2x)&lt;sup&gt;3&lt;/sup&gt;(-3)  +  (2x)&lt;sup&gt;2&lt;/sup&gt;(-3)  +  (2x)&lt;sup&gt;1&lt;/sup&gt;(-3)  +  (2x)&lt;sup&gt;0&lt;/sup&gt;(-3)

From left to right put the exponents 0,1,2,3,4 on the (-3)&#39;s

 (2x)&lt;sup&gt;4&lt;/sup&gt;(-3)&lt;sup&gt;0&lt;/sup&gt; +  (2x)&lt;sup&gt;3&lt;/sup&gt;(-3)&lt;sup&gt;1&lt;/sup&gt; +  (2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; +  (2x)&lt;sup&gt;1&lt;/sup&gt;(-3)&lt;sup&gt;3&lt;/sup&gt; +  (2x)&lt;sup&gt;0&lt;/sup&gt;(-3)&lt;sup&gt;4&lt;/sup&gt;

Put a 1 coefficient before the 1st term:

1(2x)&lt;sup&gt;4&lt;/sup&gt;(-3)&lt;sup&gt;0&lt;/sup&gt; +  (2x)&lt;sup&gt;3&lt;/sup&gt;(-3)&lt;sup&gt;1&lt;/sup&gt; +  (2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; +  (2x)&lt;sup&gt;1&lt;/sup&gt;(-3)&lt;sup&gt;3&lt;/sup&gt; +  (2x)&lt;sup&gt;0&lt;/sup&gt;(-3)&lt;sup&gt;4&lt;/sup&gt;

Look at 1st term.  Multiply that 1 coefficient by the exponent of (2x), which is 4, 
getting 1×4 = 4 and divide that 4 by 1 since that is the 1st term, getting 4.  

Put a 4 coefficient before the 2nd term

1(2x)&lt;sup&gt;4&lt;/sup&gt;(-3)&lt;sup&gt;0&lt;/sup&gt; + 4(2x)&lt;sup&gt;3&lt;/sup&gt;(-3)&lt;sup&gt;1&lt;/sup&gt; +  (2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; +  (2x)&lt;sup&gt;1&lt;/sup&gt;(-3)&lt;sup&gt;3&lt;/sup&gt; +  (2x)&lt;sup&gt;0&lt;/sup&gt;(-3)&lt;sup&gt;4&lt;/sup&gt;

Look at 2nd term.  Multiply that 4 coefficient by the exponent of (2x), which
is 3, getting 4×3 = 12 and divide that 12 by 2 since that is the 2nd term, getting 6.  

Put a 6 coefficient before the 3rd term

1(2x)&lt;sup&gt;4&lt;/sup&gt;(-3)&lt;sup&gt;0&lt;/sup&gt; + 4(2x)&lt;sup&gt;3&lt;/sup&gt;(-3)&lt;sup&gt;1&lt;/sup&gt; + 6(2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; +  (2x)&lt;sup&gt;1&lt;/sup&gt;(-3)&lt;sup&gt;3&lt;/sup&gt; +  (2x)&lt;sup&gt;0&lt;/sup&gt;(-3)&lt;sup&gt;4&lt;/sup&gt;

Look at 3rd term.  Multiply that 6 coefficient by the exponent of (2x), which
is 2, getting 6×2 = 12 and divide that 12 by 3 since that is the 3rd term, getting 4.  

Put a 4 coefficient before the 4th term

1(2x)&lt;sup&gt;4&lt;/sup&gt;(-3)&lt;sup&gt;0&lt;/sup&gt; + 4(2x)&lt;sup&gt;3&lt;/sup&gt;(-3)&lt;sup&gt;1&lt;/sup&gt; + 6(2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; + 4(2x)&lt;sup&gt;1&lt;/sup&gt;(-3)&lt;sup&gt;3&lt;/sup&gt; +  (2x)&lt;sup&gt;0&lt;/sup&gt;(-3)&lt;sup&gt;4&lt;/sup&gt;

Look at 4th term.  Multiply that 4 coefficient by the exponent of (2x), which
is 1, getting 4×1 = 4 and divide that 4 by 4 since that is the 4th term, getting 1.  

Put a 1 coefficient before the 5th term.

1(2x)&lt;sup&gt;4&lt;/sup&gt;(-3)&lt;sup&gt;0&lt;/sup&gt; + 4(2x)&lt;sup&gt;3&lt;/sup&gt;(-3)&lt;sup&gt;1&lt;/sup&gt; + 6(2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; + 4(2x)&lt;sup&gt;1&lt;/sup&gt;(-3)&lt;sup&gt;3&lt;/sup&gt; + 1(2x)&lt;sup&gt;0&lt;/sup&gt;(-3)&lt;sup&gt;4&lt;/sup&gt;

That&#39;s the answer except for simplifying:

We can erase the 1 coefficients and the 1 exponents.  We can also erase the 
factors with 0 exponents since they are 1.  Finish simplifying:

(2x)&lt;sup&gt;4&lt;/sup&gt; + 4(2x)&lt;sup&gt;3&lt;/sup&gt;(-3) + 6(2x)&lt;sup&gt;2&lt;/sup&gt;(-3)&lt;sup&gt;2&lt;/sup&gt; + 4(2x)(-3)&lt;sup&gt;3&lt;/sup&gt; + (-3)&lt;sup&gt;4&lt;/sup&gt;

16x&lt;sup&gt;4&lt;/sup&gt; + 4(8x&lt;sup&gt;3&lt;/sup&gt;)(-3) + 6(4x&lt;sup&gt;2&lt;/sup&gt;)(9) +4(2x)(-27) +(-3)&lt;sup&gt;4&lt;/sup&gt;

16x&lt;sup&gt;4&lt;/sup&gt; - 96x&lt;sup&gt;3&lt;/sup&gt; + 216x&lt;sup&gt;2&lt;/sup&gt; - 216x + 81   

Edwin&lt;/pre&gt; </PRE>