Maths Extension 1 Year 11 - Module 4 - Lesson 10
The Binomial Theorem — General Term
Name
Date
Class
1. Lesson focus
The general term. The (r+1)th term of (a+b)^n is nCr a^(n−r)b^r; solve the exponent condition before evaluating its coefficient.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Find the term containing x⁴ in (x+3)^7.
3. Find the term independent of x in (2x−1)^6.
3. Challenge
Find the coefficient of x² in (2x+1)^6.
4. Multiple choice
In (x+2)^6, which r gives the x³ term?
A. r=2
B. r=4
C. r=3
D. r=5
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Write the general term of (x+2)^7.
T_(r+1)=7Cr x^(7−r)2^r, for r=0,…,7.
2. Find the term containing x⁴ in (x+3)^7.
7−r=4 gives r=3: 7C3·3³x⁴=35·27x⁴=945x⁴.
3. Find the term independent of x in (2x−1)^6.
x exponent 6−r=0 gives r=6: (−1)^6=1.
Challenge. Find the coefficient of x² in (2x+1)^6.
6−r=2 gives r=4: 6C4·2²=15·4=60.
Multiple choice. In (x+2)^6, which r gives the x³ term?
Correct answer: C. The x exponent is 6−r. Setting it to 3 gives r=3.
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