Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Add and subtract polynomial expressions with aligned variable powers.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
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
Simplify (3x²−2x+4)−(x²+5x−6).
Why this math matters
Organize a symbolic total by the kind of dependence each term has on its input. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
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.
Combine polynomials by matching powers
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Simplify (3x²−2x+4)−(x²+5x−6).
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.
Represent the conditions
3x²−2x+4−x²−5x+6
Subtracting a group reverses the sign of every term in it.
Develop the calculation
(3−1)x²+(−2−5)x+(4+6)
Collect only terms with the same variable power.
Check and interpret
2x²−7x+10
The quadratic, linear, and constant parts remain separate algebraic units.
The result
2x²−7x+10
The quadratic, linear, and constant parts remain separate algebraic units.
Common mistakes to catch
- Determine degree after simplifying cancellations.
- A subtraction sign applies to the entire polynomial being removed.
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
Add (2t²+3) and (−2t²+5t−1).
Show a hint
The squared terms cancel.
Reveal answer and explanation
5t+2
2t²−2t²=0 and 3−1=2.
Practice 2
What is the degree of 4x³−4x³+2x²+1 after simplification?
Show a hint
Cancel equal and opposite highest-power terms first.
Reveal answer and explanation
2
The cubic terms vanish, leaving a nonzero quadratic term.
Take the idea with you
Organize a symbolic total by the kind of dependence each term has on its input.
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: Multiply every pair of binomial terms
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