Academic Team Math Practice Test 2026 - Free Math Practice Questions and Study Guide

To determine the fifth term in the binomial expansion of \((x - 3y)^8\), we can use the Binomial Theorem, which states that the expansion of \((a + b)^n\) can be expressed as:

\[

\sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k

\]

In this case, \(a = x\), \(b = -3y\), and \(n = 8\).

The general term in the expansion, often denoted as \(T_{k+1}\), is given by:

\[

T_{k+1} = \binom{n}{k} a^{n-k} b^k

\]

For the fifth term, we set \(k = 4\) (since we start counting from \(k = 0\)). Thus, we have:

\[

T_{5} = \binom{8}{4} (x)^{8-4} (-3y)^4

\]

Now, calculating each part:

1. **Calculate the binomial coefficient**:

\(\binom{8}{4} =