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Find the first 3 terms, in ascending powers of x, of the binomial expansion of (3−2x)⁵, giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2009 - Paper 2

Question 3

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (3−2x)⁵, 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 (3−2x)⁵, giving each term in its simplest form. - Edexcel - A-Level Maths Pure - Question 3 - 2009 - Paper 2

Step 1

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Answer

To find the first term of the binomial expansion, we use the formula for the binomial theorem:

$inom{n}{k} a^{n-k} b^k$

For our expression $(3 - 2x)^5$ , where $a = 3$ , $b = -2x$ , and $n = 5$ , the first term (when $k=0$ ) is:

$inom{5}{0} (3)^5 (-2x)^0 = 1 imes 243 imes 1 = 243.$

Step 2

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Answer

For the second term (when $k=1$ ):

$inom{5}{1} (3)^{5-1} (-2x)^1 = 5 imes 81 imes (-2x) = -810x.$

Step 3

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Answer

For the third term (when $k=2$ ):

$inom{5}{2} (3)^{5-2} (-2x)^2 = 10 imes 27 imes 4x^2 = 1080x^2.$

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