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What is the coefficient of $xy$ in the expansion of $(3x+(2y+1))^2$?

Mellie  May 9, 2015

Best Answer 

 #1
avatar+78741 
+15

 $$$(3x+(2y+1))^2$$

This term would be

C(2,1)*(3x)^1 *(2y + 1)^1  =

2(3x)(2y + 1) =

6x(2y + 1) =

12xy + 6x

So....the coefficient is 12

 

  

CPhill  May 9, 2015
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2+0 Answers

 #1
avatar+78741 
+15
Best Answer

 $$$(3x+(2y+1))^2$$

This term would be

C(2,1)*(3x)^1 *(2y + 1)^1  =

2(3x)(2y + 1) =

6x(2y + 1) =

12xy + 6x

So....the coefficient is 12

 

  

CPhill  May 9, 2015
 #2
avatar+91045 
+10

Thanks Chris,

This can be easily done by any good yr 9 student.

 

$$\\\boxed{(a+b)^2=a^2+2ab+b^2}\\\\
so\\\\
(3x+(2y+1))^2\\
=(3x)^2+2*3x*(2y+1)+(2y+1)^2\\
=etc\\\\
$The only term with xy is going to be $ \\
2*3x*2y=12xy\\
$so the coefficient of xy is 12$$$

Melody  May 10, 2015

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