Question 74227
The binomial expansion uses Pascal's triangle to find the coefficients. The general form of the expansion (x+y)^n is 
*[Tex \Large a_0 x^ny^0+a_1x^{n-1}y^1 \ldots a_n x^0y^n] 
Where *[Tex \Large a_n] is the coefficient. So we would use Pascals triangle to find the coefficients.
If you look at the 8th row of Pascal's triangle you would see
<pre> 1     8     28    56    70    56    28    8    1 </pre>
So each number in this row is our *[Tex \Large a_n] which is to be multiplied by our terms.

So our expansion is *[Tex \Large x^83^0+8x^73^1+28x^63^2+56x^53^3]And we can see that 56*3^3 is our coefficient. Or in other words since our fifth term is 
*[Tex \Large 1512x^5] our coefficient is 1512