Question 1206241
<br>
(NOTE: The answer is not 96....)<br>
Here are the first several rows of Pascal's Triangle:<br><pre>

                   1  <------------- row 0
                 1   1  <----------- row 1
               1   2   1  <--------- row 2
             1   3   3   1  <------- row 3
           1   4   6   4   1  <----- row 4
         1   5  10  10   5   1  <--- row 5</pre>
The numbers in row n are the coefficients of the expansion of {{{(a+b)^n}}}.<br>
For example, the "1 3 3 1" in row 3 are the coefficients in the expansion of {{{(a+b)^3=(1)(a^3)+(3)(a^2)(b)+(3)(a)(b^2)+(1)(b^3)}}}<br>
Your expression is {{{2x+2)^4}}}, so you are interested in the numbers in row 4 of Pascal's Triangle.  Using your expression {{{2x+2)}}} and the numbers in row 4....<br>
{{{(2x+2)^4=(1)((2x)^4)+(4)((2x)^3)(2)+(6)((2x)^2)(2)^2+(4)((2x)^1)(2)^3+(1)(2)^4}}}<br>
You are asked for the coefficient of the x term.  That term is {{{(4)((2x)^1)(2)^3}}}; the coefficient is {{{(4)(2)((2^3))=4*2*8=64}}}.<br>