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What is the value of the 4th term of the expansion (a+b)^5

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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 \(10 \cdot a^2 \cdot b^3\).

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