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Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 + x)^6, giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2006 - Paper 2

Question 3

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 + x)^6, giving each term in its simplest form.

Worked Solution & Example Answer:Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 + x)^6, giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2006 - Paper 2

Step 1

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Answer

To find the first term of the binomial expansion of ((2 + x)^6), we use the formula for the binomial theorem, which is given by:

$C(n, k) a^{n-k} b^{k}$

For the first term where (k = 0), we have:

$C(6, 0) \cdot 2^{6} \cdot x^{0} = 1 \cdot 64 \cdot 1 = 64$

Thus, the first term is (64).

Step 2

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Answer

For the second term where (k = 1):

$C(6, 1) \cdot 2^{6-1} \cdot x^{1} = 6 \cdot 32 \cdot x = 192x$

Thus, the second term is (192x).

Step 3

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Answer

For the third term where (k = 2):

$C(6, 2) \cdot 2^{6-2} \cdot x^{2} = 15 \cdot 16 \cdot x^{2} = 240x^{2}$

Thus, the third term is (240x^{2}).

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