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

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+1773

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

Mellie  May 9, 2015

#1
+84385
+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
Sort:

#1
+84385
+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
#2
+91972
+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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