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 Feb 10, 2020
 #1
avatar+111389 
+2

We have

 

(2x^2  - 3y)^3  =

 

C(3,0)(2x^3)^3 * (3y)^0   -  C(3,1) (2x^3)^2(3y)^1  + C(3,2)(2x^3)^1 (3y)^2  + C(3,3)(2x^3)^0 (3y)^3  =

 

 

   1   (8x^9)   -   3 (4x^6)(3y)  +  3 (2x^3)(9y^2)  + 1 ( 27y^3) 

 

The coefficients are in  red

 

And the final expansion is

 

 

8x^9  - 36x^6y + 54x^3y^2 - 27y^3

 

 

cool cool cool

 Feb 10, 2020
edited by CPhill  Feb 10, 2020
 #2
avatar+12269 
+4

With pascal's triangel:

 Feb 10, 2020

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