Find the first 4 terms, in ascending powers of x, of the binomial expansion of
\(
\left(3 - \frac{1}{3} x \right)^5
\)
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 3
Question 3
Find the first 4 terms, in ascending powers of x, of the binomial expansion of
\(
\left(3 - \frac{1}{3} x \right)^5
\)
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
\(
\left(3 - \frac{1}{3} x \right)^5
\)
giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 3
Step 1
Find the First Term
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Answer
The first term of the binomial expansion is given by:
(05)(3)5(−31x)0=1⋅243⋅1=243.
Thus, the first term is 243.
Step 2
Find the Second Term
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Answer
The second term is given by:
(15)(3)4(−31x)1=5⋅81⋅(−31x)=−135x.
Thus, the second term is -135x.
Step 3
Find the Third Term
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Answer
The third term is:
(25)(3)3(−31x)2=10⋅27⋅91x2=30x2.
Thus, the third term is 30x².
Step 4
Find the Fourth Term
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