[Maximum mark: 6]
(a) Write down and simplify the expansion of $(2+x)^{4}$ in ascending powers of $x$.
Answer
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Answer
Simplify the terms: \(\boxed{16 + 32x + 24x^2 + 8x^3 + x^4}\)
Steps
Step 1 ：Use the binomial theorem to expand $(2+x)^4$: \(\sum_{k=0}^{4} \binom{4}{k} 2^{4-k} x^k\)
Step 2 ：Simplify the terms: \(\boxed{16 + 32x + 24x^2 + 8x^3 + x^4}\)
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