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avatar+366 

Help me, please

 

Binomial Theorem: find the indicated term of the expansion

 

4th term of (4x - y)^9

ManuelBautista2019  Jan 29, 2018
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 #1
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(4x  - y ) ^9          4th term

 

Note the  pattern, Manuel

 

C(9,0) * (4x)^9 *y^0  -   C(9,1) * (4x)^8 * y^1  +  C(9,2) * (4x)^7 * (y)^2  - C(9,3) *(4x)^6 * y^3

 

The   exponents  always sum to the expansion power and   in the form (a - b)^n, the terms alternate signs from positive, negative, positive, etc. 

 

We are interested in the term in red...so we have

 

- C(9,3) * (4x)^6 * y^3   =

 

- 84  * 4096 x^6 y^3  =

 

- 344064 x^6 y^3

 

Here's the expansion  as a check :

 

262144 x^9 - 589824 x^8 y + 589824 x^7 y^2 - 344064 x^6 y^3 + 129024 x^5 y^4 - 32256 x^4 y^5 + 5376 x^3 y^6 - 576 x^2 y^7 + 36 x y^8 - y^9

 

 

cool cool cool

CPhill  Jan 29, 2018

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