Learn with Amar
Teaching video
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Grade 11 chapters and video availability01 · Read and understand
What you will learn
- Combine choice counts with power factors in the binomial theorem.
- Justify the conclusion "The coefficient is 10·8=80" using the stated assumptions.
Before you start
Combinations and polynomial products.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Find the coefficient of x³ in (1+2x)⁵.
Why this math matters
Combine choice counts with power factors in the binomial theorem. This worked micro-lesson connects a precise mathematical condition to a conclusion you can check. The transfer task asks you to change the setting and decide which parts of the reasoning still apply.
Set up the model
A useful answer starts with clear assumptions:
- The exponent is a nonnegative integer.
- Ordinary commuting polynomial multiplication is used.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Select one coefficient without expanding every term
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find the coefficient of x³ in (1+2x)⁵.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Build the model
An x³ term chooses 2x from exactly three of five factors
The remaining factors contribute one.
Work through the mathematics
There are C(5,3)=10 choices, each contributing 2³x³
Selection count and coefficient product are separate factors.
Check the conclusion
The coefficient is 10·8=80
Every selection has the same contribution, so their coefficients add.
The result
The coefficient is 10·8=80
Every selection has the same contribution, so their coefficients add.
Common mistakes to catch
- Do not omit the coefficient raised to the selected power.
- A coefficient excludes the variable factor itself.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find the coefficient of x² in (1+3x)⁴.
Show a hint
Choose two factors and multiply by 3².
Reveal answer and explanation
54
C(4,2)·9=6·9.
Practice 2
What is the constant term of (2+x)⁶?
Show a hint
Choose no x factors.
Reveal answer and explanation
64
All six factors contribute two.
Take the idea with you
Count contributions to a target degree in a repeated-product model.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Recognize quadratic sequences from their differences
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