Find the first three 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 - 2005 - Paper 2
Question 3
Find the first three 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 three 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 - 2005 - Paper 2
Step 1
Step 1: Identify the expansion terms
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Answer
The binomial expansion of (a + b)ⁿ can be expressed using the Binomial Theorem as:
(a+b)n=∑k=0n(kn)an−kbk
For our case, a = 3, b = 2x, and n = 5.
Step 2
Step 2: Calculate the first three terms
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Answer
Using the Binomial Theorem:
For k = 0:
(05)(3)5(2x)0=1⋅243⋅1=243
For k = 1:
(15)(3)4(2x)1=5⋅81⋅(2x)=810x
For k = 2:
(25)(3)3(2x)2=10⋅27⋅(4x2)=1080x2
Step 3
Step 3: Write the result
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Answer
Combining these terms, the first three terms of the binomial expansion are:
