Learn with Amar
Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to distribute a negative factor to every term.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Signed multiplication and substitution.
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 −3(2x − 5) and check the expression when x = 4.
Why this math matters
Distributivity multiplies every term inside a grouped sum by the outside factor, including its sign. Use a numerical substitution to catch distribution errors before solving a longer equation.
Set up the model
A useful answer starts with clear assumptions:
- x can be any real number.
- Juxtaposition next to parentheses denotes multiplication.
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.
Distribute a negative factor to every term
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Simplify −3(2x − 5) and check the expression when x = 4.
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 quantities
−3(2x − 5) = (−3)(2x) + (−3)(−5)
Treat subtraction inside the parentheses as adding a negative term.
Apply the relationship
= −6x + 15
The first product is negative; the product of the two negatives is positive.
Check and interpret
x = 4: −3(8 − 5) = −9; −24 + 15 = −9
Both forms agree at the test input, consistent with the distributive identity.
The result
x = 4: −3(8 − 5) = −9; −24 + 15 = −9
Both forms agree at the test input, consistent with the distributive identity.
Common mistakes to catch
- Distributing only to the first term changes the expression.
- A minus outside parentheses applies to every term, not just the nearest letter.
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
Expand 4(3 − 2y).
Show a hint
Multiply 4 by both terms.
Reveal answer and explanation
12 − 8y
4 × 3 = 12 and 4 × (−2y) = −8y.
Practice 2
Which expression equals −(a + 7): −a + 7 or −a − 7?
Show a hint
The leading minus is a factor of −1.
Reveal answer and explanation
−a − 7
Multiplication by −1 changes the sign of each term inside the parentheses.
Take the idea with you
Use a numerical substitution to catch distribution errors before solving a longer equation.
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: Combine quantities with matching variable parts
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