Question 1141509
.
<pre>
The binomial expansion is this formula


    {{{(x+y)^n}}} = {{{x^n}}} + {{{C[n]^1*x^(n-1)*y}}} + {{{C[n]^2*x^(n-2)*y^2}}} + {{{C[n]^3*x^(n-3)*y^3}}} + . . . + {{{C[n]^(n-1)*x^1*y^(n-1)}}} + {{{y^n}}}


In our case,  n = 20,  x = ab,  y = -1,  therefore, the common term of the binomial expansion in our case is  


    {{{C[20]^k*(ab)^(20-k)*(-1)^k}}}, k = 0, 1, 2, 3, 4, 5, . . . 


Then the 5-th term is at k = 4 


    {{{C[20]^4*(ab)^(20-4)*(-1)^4}}} = {{{((20*19*18*17)/(1*2*3*4))*(ab)^16}}} = {{{4845*a^16*b^16}}}.
</pre>

--------------


If you want to see other similar solved problems and to learn the subject wider and deeper, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Permutations/Solved-problems-on-binomial-coefficients.lesson>Solved problems on binomial coefficients</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this textbook under the topic
"<U>Binomial expansion, binomial coefficients, Pascal's triangle</U>".



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.