Question

use the Binomial Theorem to find the binomial expansion of the expression (d+3)^7

Answer 1

\[\huge (1+x)^n=[1+nx+\frac{(n)(n-1)}{2!}(x)^2+\frac{(n)(n-1)(n-2)}{3!}(x)^3+...+x^n]\]

Answer 2

a. d^7 +21d^6 +189d^5 + 945d^4 + 2835d^3 + 5103d^2 +5103d + 2187
b. d^7 - 7d^6 - 21d^5 - 35d^4 +35d^3 -20d^2 +7d -1
c. d^7 + 7d^6 +21d^5 +35d^4 +35d^3 +20d^2 +7d +1
d.d^7-21d^6+189d^5-945d^4+2835d^3-5103d^2+5103d-2187

Answer 3

oh first move the 3 out of the bracket

Answer 4

\[\huge (3+d)^7 \\ \\ \huge 3^7(1+\frac{d}{7})^7\]

Answer 5

@.Sam. Isn't that wrong? I mean, it should be\[3^7\left(1 + \dfrac{d}{3}\right)^7\]

Answer 6

Yeah whoops

Answer 7

i think its either a or d. but im honestly not sure

Answer 8

So just sub into it, x=d/3, n=7
\[\huge 3^7[1+7(\frac{d}{3})+\frac{(7)(7-1)}{2}(\frac{d^2}{9})+\frac{(7)(7-1)(7-2)}{6}(\frac{d^3}{27})...]\]