Expand (2x + 1)^12
4096 x^12 + 24576 x^11 + 67584 x^10 + 112640 x^9 + 126720 x^8 + 101376 x^7 + 59136 x^6 + 25344 x^5 + 7920 x^4 + 1760 x^3 + 264 x^2 + 24 x + 1
+1094 Or, instead of expanding, which could be very messy, and probably best done with an online calculator, we can use the binomial theorem. <------ a link to what that is
Anways, assuming you now understand what the binomial theorem is, we can solve the problem.
We see that the 5th power in an expansion is: (n C n-5) * x^5 * y ^[n-5]
In this case:
n = 12
y = 1
x = 2x (which is weird, but the second 'x' is a value, while the first is a placeholder)
Plug those values in:
(12 C 7) * (2x)^5 * 1^7 =
792 * 32x^5 =
25344x^5
:)
