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What is the coefficient of \(x^2y^2\) in the expansion of \((x+y)^4+(x+2y)^4 \)?

 Dec 31, 2017
 #1
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(x + y)^4  =  x^4  + 4x^3y + 6x^2y^2   + 4xy^3  + y^4

 

(x + 2y)^4   =  x^4  +  4x^3*2y  +  6x^2*(2y)^2  +  4x*(2y)^3  + (2y)^4

 

So.....the sum of the x^2y^2  terms is

 

6x^2y^2  +  6x^2* (2y)^2  =

 

6x^2y^2 +  24x^2y^2  =

 

30

 

 

cool cool cool

 Dec 31, 2017

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