[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: $16 + 32 x + 24 x^{2} + 8 x^{3} + x^{4}$

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: $16 + 32 x + 24 x^{2} + 8 x^{3} + x^{4}$