Question 144799
<pre><font size = 4 color = "indigo"><b>
{{{(r-2s)^8=(matrix(2,1,8,0))r^8 + (matrix(2,1,8,1))r^7(-2s) + (matrix(2,1,8,2))r^6(-2s)^2+(matrix(2,1,8,3))r^5(-2s)^3+(matrix(2,1,8,4))r^4(-2s)^4+(four_more_terms)}}}

{{{(r-2s)^8=(Z)r^8 + (Z)r^7(-2s) + (Z)r^6(-2s)^2+(Z)r^5(-2s)^3+(Z)r^4(-2s)^4+(four_more_terms)}}}

{{{(matrix(2,1,8,0)) = 1}}}

{{{(matrix(2,1,8,1)) = 8!/(1!7!) = (8*7*6*5*4*3*2*1)/(1*7*6*5*4*3*2*1)=

(8*cross(7*6*5*4*3*2*1))/(1*cross(7*6*5*4*3*2*1))=8/1=8}}}

{{{(matrix(2,1,8,2)) = 8!/(2!6!) = (8*7*6*5*4*3*2*1)/(2*1*6*5*4*3*2*1)=

(8*7*cross(6*5*4*3*2*1))/(2*1*cross(6*5*4*3*2*1))=(8*7)/(2*1)=28}}}

{{{(matrix(2,1,8,3)) = 8!/(3!5!) = (8*7*6*5*4*3*2*1)/(3*2*1*5*4*3*2*1)=

(8*7*6*cross(5*4*3*2*1))/(3*2*1*cross(5*4*3*2*1))=(8*7*6)/(3*2*1)=(8*7*cross(6))/(cross(3*2)*1)=56}}}

{{{(matrix(2,1,8,4)) = 8!/(4!4!) = (8*7*6*5*4*3*2*1)/(4*3*2*1*4*3*2*1)=

(8*7*6*5*cross(4*3*2*1))/(4*3*2*1*cross(4*3*2*1))=(8*7*6*5)/(4*3*2*1)=(cross(8)*7*6*5)/(cross(4)*3*cross(2)*1)=70}}}

{{{(r-2s)^8=(1)r^8 + (8)r^7(-2s) + (28)r^6(-2s)^2+(56)r^5(-2s)^3+(70)r^4(-2s)^4+(four_more_terms)}}}

{{{(r-2s)^8=r^8 + 8r^7(-2s) + 28r^6(4s^2)+56r^5(-8s^3)+70r^4(16s^4)+(four_more_terms)}}}

{{{(r-2s)^8=r^8 - 16r^7s + 112r^6s^2-424r^5s^3+1120r^4s^4+(four_more_terms)}}}

Edwin</pre>