The first three terms, in ascending powers of x, of the binomial expansion of
(9 + 2x)^2 are given by
(9 + 2x)^2 ≈ a + \frac{x}{3} - \frac{x^2}{54}
where a is a constant - AQA - A-Level Maths Mechanics - Question 1 - 2020 - Paper 1
Question 1
The first three terms, in ascending powers of x, of the binomial expansion of
(9 + 2x)^2 are given by
(9 + 2x)^2 ≈ a + \frac{x}{3} - \frac{x^2}{54}
where a is ... show full transcript
Worked Solution & Example Answer:The first three terms, in ascending powers of x, of the binomial expansion of
(9 + 2x)^2 are given by
(9 + 2x)^2 ≈ a + \frac{x}{3} - \frac{x^2}{54}
where a is a constant - AQA - A-Level Maths Mechanics - Question 1 - 2020 - Paper 1
Step 1
State the range of values of x for which this expansion is valid.
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Answer
The binomial expansion is valid under the condition that the absolute value of the term inside the brackets remains less than 1. Therefore, we have:
∣92x∣<1
Solving this gives us:
∣x∣<29
So, the correct answer is:
∣x∣<29
Step 2
Find the value of a.
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Answer
To find the value of a, we evaluate the constant term in the binomial expansion:
The first term of the expansion, when x = 0, is (9)^2, which equals 81. Thus:
