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Find the first 3 terms, in ascending powers of x, of the binomial expansion of (3 - x)^6 and simplify each term. - Edexcel - A-Level Maths Pure - Question 3 - 2010 - Paper 4

Question 3

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (3 - x)^6 and simplify each term.

Worked Solution & Example Answer:Find the first 3 terms, in ascending powers of x, of the binomial expansion of (3 - x)^6 and simplify each term. - Edexcel - A-Level Maths Pure - Question 3 - 2010 - Paper 4

Step 1

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Answer

Using the binomial theorem, the first term in the expansion of ((3 - x)^6) is given by:

$T_0 = \binom{6}{0} (3)^{6} (-x)^{0} = 729$ .

Step 2

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Answer

The second term in the expansion is:

$T_1 = \binom{6}{1} (3)^{5} (-x)^{1} = 6 \cdot 243 \cdot (-x) = -1458x$ .

Step 3

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Answer

The third term in the expansion is:

$T_2 = \binom{6}{2} (3)^{4} (-x)^{2} = 15 \cdot 81 \cdot x^{2} = 1215x^{2}.$

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