74.6k views
4 votes
Consider the expansion of (3x + 2y)^4 What is the coefficient of the xy^3 term?

1 Answer

5 votes

The given expression is:


(3x+2y)^4

This can be expanded as:


\begin{gathered} (3x+2y)^4=4C0(3x)^4(2y)^0+4C1(3x)^3(2y)^1 \\ +4C2\mleft(3x\mright)^2\mleft(2y\mright)^2+4C3\mleft(3x\mright?^{})^1(2y)^3+4C4(3x)^0(2y)^4 \end{gathered}

Note that:


\begin{gathered} \text{nCr}=\text{ }(n!)/((n-r)!r!) \\ 4C0=\text{ 1} \\ 4C1=4 \\ 4C2=6 \\ 4C3=4 \\ 4C4=1 \end{gathered}

The expansion then becomes:


(3x+2y)^4=\text{ }81x^4+216x^3y+216x^2y^2+96xy^3+16y^4

User Udi Meiri
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories