Binomial Expansion

Question

The 4th term in the expansion of (x + 2)⁶ is

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To find the specific term in a binomial expansion:
1. **General Term Formula**: The $(r+1)^{th}$ term in $(a+b)^n$ is given by $T_{r+1} = \binom{n}{r} a^{n-r} b^r$.
2. **Identify Variables**: For $(x+2)^6$, we have $a = x, b = 2, n = 6$.
3. **Apply for 4th Term**: For the $4^{th}$ term, $r+1 = 4 \implies r = 3$.
4. **Calculation**:
   - $T_4 = \binom{6}{3} x^{6-3} (2)^3$
   - $\binom{6}{3} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$
   - $T_4 = 20 	imes x^3 	imes 8 = 160x^3$.

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