Maths Extension 1 Year 11 - Module 4 - Lesson 9
The Binomial Theorem — Expansion
Name
Date
Class
1. Lesson focus
Binomial expansion. For a positive integer n, (a+b)^n=Σ(nCr)a^(n−r)b^r; the power of a falls as the power of b rises.
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 coefficient of x³ in (2x−1)^5.
3. Find the constant term in (x+3)^6.
3. Challenge
Expand (2x+1)^4.
4. Multiple choice
The coefficient of x² in (x+1)^5 is?
A. 5
B. 10
C. 15
D. 20
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Expand (x+2)^4.
x⁴+8x³+24x²+32x+16.
2. Find the coefficient of x³ in (2x−1)^5.
Choose the term with (−1)^2: 5C2(2x)^3(−1)^2=80x³; coefficient 80.
3. Find the constant term in (x+3)^6.
Choose x⁰: 3⁶=729.
Challenge. Expand (2x+1)^4.
16x⁴+32x³+24x²+8x+1.
Multiple choice. The coefficient of x² in (x+1)^5 is?
Correct answer: B. General term 5Cr x^(5−r); x² occurs at r=3, giving 5C3=10.
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