Question

Write the fifteenth term of the binomial expansion of (a³+d) 24.

Answer 1

Answer: 1,961,256a³⁰d¹⁴

Explanation:

`\displaystyle\\(x+y)^n \ is\ the\ binomial\ expansion \\\\The\ k\ term =C_n^(k-1)x^(n-k+1)y^(k-1)\\\\ n - the\ power \ of\ the \ binomial\\\\k - number\ of\ the\ term \ of\ the\ binomial`

`(a^3+d)^(24)`

`The \ fifteenth\ term=C^(15-1)_ {24}(a^3)^(24-15+1)d^(15-1)\\\\The \ fifteenth\ term=C^(14)_(24)(a^3)^(10)d^(14)\\\\The \ fifteenth\ term=(24!)/((24-14)!14!) a^(30)d^(14)\\\\The \ fifteenth\ term=(24!)/(10!14!)a^(30)d^(14) \\\\The \ fifteenth\ term=1,961,256 a^(30)d^(14)`

Answer 2

a^45d^9

To find the fifteenth term of the binomial expansion of (a³+d)24, we can use the binomial theorem, which states that the expansion of (a+b)n is given by the sum of the terms in the following formula:

(a+b)^n = a^n + na^(n-1)b + (n(n-1))/2a^(n-2)*b^2 + ... + b^n