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Find the term containing x^5 in the expansion of (2x+1)^12

 Aug 26, 2020
 #1
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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
 

 Aug 26, 2020
 #2
avatar+1039 
+1

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


:)
 

 Aug 26, 2020

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