Explanation:
The expansion of \((a+b)^5\) can be calculated using the binomial theorem, which states that the \(k\)-th term in the expansion is given by:
\[\binom{n}{k} \cdot a^{n-k} \cdot b^k\]
In the case of \((a+b)^5\), where \(n = 5\), the \(k\)-th term is:
\[\binom{5}{k} \cdot a^{5-k} \cdot b^k\]
For the 4th term (\(k = 3\)), the expression becomes:
\[\binom{5}{3} \cdot a^{5-3} \cdot b^3\]
Now, calculate the values:
\[\binom{5}{3} = \frac{5!}{3!(5-3)!} = 10\]
\[a^{5-3} = a^2\]
\[b^3 = b^3\]
So, the 4th term of the expansion is \(10 \cdot a^2 \cdot b^3\).