Find the first 3 terms, in ascending powers of $x$, in the binomial expansion of
$(2 - 5x)^6$ - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 6
Question 3
Find the first 3 terms, in ascending powers of $x$, in the binomial expansion of
$(2 - 5x)^6$.
Give each term in its simplest form.
Worked Solution & Example Answer:Find the first 3 terms, in ascending powers of $x$, in the binomial expansion of
$(2 - 5x)^6$ - Edexcel - A-Level Maths Pure - Question 3 - 2013 - Paper 6
Step 1
Find the first term:
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Answer
Using the binomial theorem, the first term when k=0 is:
T_0 = inom{6}{0} (2)^{6} (-5x)^{0} = (2)^{6} = 64.
Step 2
Find the second term:
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Answer
For the second term when k=1, we have:
T_1 = inom{6}{1} (2)^{5} (-5x)^{1} = 6 \times 32 \times (-5x) = -960x.
Step 3
Find the third term:
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Answer
For the third term when k=2, we get:
T_2 = inom{6}{2} (2)^{4} (-5x)^{2} = 15 \times 16 \times 25x^{2} = 6000x^{2}.
