Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of
$$
\left( 2 - \frac{1}{2} x \right) ^8
$$
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 5
Question 5
Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of
$$
\left( 2 - \frac{1}{2} x \right) ^8
$$
giving each term in its simplest form.
Worked Solution & Example Answer:Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of
$$
\left( 2 - \frac{1}{2} x \right) ^8
$$
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 5 - 2013 - Paper 5
Step 1
Find the first term using the Binomial Theorem
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Answer
The first term of the expansion is given by the formula:
(0n)anb0=(08)(2)8(−21x)0=256
Thus, the first term is 256.
Step 2
Find the second term
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Answer
The second term is:
(18)an−1b1=(18)(2)7(−21x)1=8⋅128⋅(−21x)=−512x
So, the second term is -512x.
Step 3
Find the third term
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Answer
The third term can be calculated as:
(28)an−2b2=(28)(2)6(−21x)2=28⋅64⋅41x2=448x2
Thus, the third term is 448x².
Step 4
Find the fourth term
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