Finding the coefficient a of the term in the expansion of the binomial.

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) *

a =  (12! /(8! * 4!) ) *

a = ( 12*11*10*9/  4*3*2*1)  *

a =  (11*5*9) *

a = 11*5*9 * 6561

a = 3,247,695

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.