Question

Finding the coefficient a of the term in the expansion of the binomial.3%29%5E%7B12%7D%20ax%5E%7B8%7D" id="TexFormula1" title="(x^{2} + 3)^{12} ax^{8}" alt="(x^{2} + 3)^{12} ax^{8}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

3,247,695

Step-by-step explanation:

We want the coefficient of  the term with  x^8

So  Use Newton's Binomial Expansion formula

Formula is  (x + y) ^n  =   Sum for i=0 to n     (n choose i)   x^(n-i)*y^i

here   (x^2  + 3) ^ 12

( 12 choose i) *  (x^2)^(12-i) * (3)^i

i needs to equal 8  for us to get  x^8

(12 choose 8) * (x^2)^(12-8) * (3^8)

= (12 choose 8) * x^8  * (3^8)

so  a = (12 choose 8) * $3^{8}$

a =  (12! /(8! * 4!) ) * $3^{8}$

a = ( 12*11*10*9/  4*3*2*1)  * $3^{8}$

a =  (11*5*9) * $3^{8}$

a = 11*5*9 * 6561

a = 3,247,695