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) * [tex]3^{8}[/tex]
a = (12! /(8! * 4!) ) * [tex]3^{8}[/tex]
a = ( 12*11*10*9/ 4*3*2*1) * [tex]3^{8}[/tex]
a = (11*5*9) * [tex]3^{8}[/tex]
a = 11*5*9 * 6561
a = 3,247,695
