Find the fourth term in the expansion of \((3x - y)^{6}\).
Question 1 Report
Find the fourth term in the expansion of \((3x - y)^{6}\).
Answer Details
To find the fourth term in the expansion of \((3x - y)^6\), we can use the binomial theorem, which states that the \(r\)th term in the expansion of \((a+b)^n\) is given by:
\[\binom{n}{r}a^{n-r}b^r\]
In this case, \(a = 3x\) and \(b = -y\) (note the negative sign). So, using the binomial theorem, the fourth term in the expansion of \((3x - y)^6\) is:
\[\binom{6}{3}(3x)^3(-y)^3 = \frac{6!}{3!3!}(27x^3)(-y^3) = -540x^3y^3\]
Therefore, the answer is \(-540x^{3}y^{3}\).
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