Find the first 3 terms, in ascending powers of $x$, of the binomial expansion of \( \left( 2 - \frac{x}{4} \right)^{10} \) giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2015 - Paper 2
Question 3
Find the first 3 terms, in ascending powers of $x$, of the binomial expansion of \( \left( 2 - \frac{x}{4} \right)^{10} \) giving each term in its simplest form.
Worked Solution & Example Answer:Find the first 3 terms, in ascending powers of $x$, of the binomial expansion of \( \left( 2 - \frac{x}{4} \right)^{10} \) giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2015 - Paper 2
Step 1
Find the first term
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Answer
The first term of the binomial expansion is given by the formula ( a^{n} ) where ( a = 2 ) and ( n = 10 ). Therefore, the first term is:
210=1024.
Step 2
Find the second term
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Answer
The second term can be calculated using the formula ( \binom{n}{k} a^{n-k} b^{k} ), where ( n = 10 ), ( k = 1 ), ( a = 2 ), and ( b = -\frac{x}{4} ). This leads to:
(110)⋅29⋅(−4x)=10⋅512⋅(−4x)=−1280x.
Step 3
Find the third term
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