The question of the topic
Nudge a factor, move the answer
Take 23 times 27, which is 621. Raise 27 to 28 and the product grows by 23.
📚 Chapter Learning Kit
We Distribute, Yet Things Multiply · Class 8 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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✏️ Example
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The whole idea, one bite at a time
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Distributing over a sum
The property that does the work
Multiplying a number by a sum equals multiplying by each part and adding.
Seeing it rather than trusting it
A block of dots
Make a rows of dots, with b columns beside c columns.
The property is not limited to two
A bracket may hold any number of terms
Take 3a times the bracket a minus b plus 5, and multiply each term inside by 3a.
What like terms are
Same letters, or stay apart
Terms carrying exactly the same letters are like terms, and only those may be joined.
Not just the letter
The powers must match too
The expression 5w squared plus 6w shares the letter w but not the power.
📖 Smart notes
What you'll study, topic by topic
1
Distributing, and how a product moves
Nudge one number in a product and the answer moves by a predictable amount. One identity covers every nudge, up or down, because a minus is only a plus with a negative number.
- The distributive property says a times a sum is the sum of the products.
- Raising one factor by 1 raises the product by the other factor.
- Raising both by 1 raises the product by a plus b plus 1.
~35 min · full explanation, examples & memory tricks in the app
2
Opening brackets, like terms and quick products
Every bracket opens the same way: each term meets each term. Then only terms with identical letters may be joined. The same property turns multiplying by 11 into a single line of digit sums.
- The distributive property is not limited to two terms in a bracket.
- Terms carrying exactly the same letters are called like terms.
- Only like terms may be joined into one.
~35 min · full explanation, examples & memory tricks in the app
3
Three identities, and what they are for
Three expansions turn up so often that they are worth knowing by heart. Each one can be seen as an area, each one follows from opening brackets, and together they make awkward arithmetic easy.
- The square of a sum is a squared plus 2ab plus b squared.
- A square of side 65 splits into 60 squared, 5 squared and two rectangles.
- The square of a difference is a squared minus 2ab plus b squared.
~35 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Multiplying a number by a sum gives the same answer as multiplying it by each part and adding. This is called
Beginner
A the distributive property
B the commutative property
C the associative property
D the identity property
Show answer & explanation
the distributive property
In letters it says a times b plus c equals ab plus ac.
The product 23 times 27 is 621. If 27 is raised to 28, the product grows by
Beginner
A 27
B 23
C 1
D 51
Show answer & explanation
23
Multiplying by 28 rather than 27 means one more lot of 23.
In general, a times the quantity b plus 1 works out as
Intermediate
A ab plus b, the same factor added once
B ab plus 1, with just one more unit added
C ab plus a plus b, with both of them added
D ab plus a, the other factor added once
Show answer & explanation
ab plus a, the other factor added once
Distributing over the bracket gives a times b and a times 1.
A block of dots has a rows, with b columns beside c columns. Counting it in two pieces gives
Intermediate
A ab dots plus ac dots
B ab dots plus bc dots
C a dots plus b dots plus c dots
D abc dots altogether
Show answer & explanation
ab dots plus ac dots
One block counted two ways is why the two expressions must agree.
🃏 Flashcards
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51 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
Play your way through this kit
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Memory Match
Word Match
Categorization
Fact Or Myth
Sequence Builder
Playable in the app
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