Schooling · Class 8 · Mathematics · We Distribute, Yet Things Multiply · Chapter on a page
CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-I
We Distribute, Yet Things Multiply: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- The distributive property states…
- The property also works with…
- You can use this property in both…
- For algebraic expressions, 2(x + 4)…
- The distributive property helps in…
- When multiplying two binomials like…
- The property holds for all real…
- Formulas and facts
- Distributive law (addition)
- Distributive law (subtraction)
- Expanding two brackets
- Factoring out
- Watch out for
- Forgetting to multiply every term…
- Ignoring the minus sign when…
- Writing 2(x + 5) = 2x + 5 instead of…
- Thinking the distributive property…
- Mixing up distribution with simple…
What this chapter is about
This chapter explores the distributive property of multiplication over addition and subtraction. You have already learnt how to multiply and add numbers, but now you will see how these two operations work together in a beautiful way. When you multiply a number with a sum (or difference), you can "distribute" the multiplication to each part separately and then combine the results.
Key ideas
- The distributive property states that a × (b + c) = a × b + a × c. Multiplication "spreads" over each term inside the bracket.
- The property also works with subtraction: a × (b − c) = a × b − a × c.
- You can use this property in both directions: expand brackets (distribute) or factor out a common term (the reverse process).
- For algebraic expressions, 2(x + 4) means 2 × x + 2 × 4 = 2x + 8.
- The distributive property helps in mental maths by breaking numbers into convenient parts.
- When multiplying two binomials like (a + b)(c + d), you distribute each term of the first bracket to each term of the second.
- The property holds for all real numbers, including negative numbers and fractions.
Formulas and facts to remember
- Distributive law (addition): a × (b + c) = a × b + a × c — multiply the outside number with each term inside, then add.
- Distributive law (subtraction): a × (b − c) = a × b − a × c — multiply the outside number with each term inside, then subtract.
- Expanding two brackets: (a + b)(c + d) = ac + ad + bc + bd — each term in the first bracket multiplies each term in the second.
- Factoring out: ab + ac = a(b + c) — the reverse of distribution; take out the common factor.
Common mistakes
- Forgetting to multiply every term inside the bracket → Always distribute the multiplier to each term, not just the first one.
- Ignoring the minus sign when distributing → Carry the sign of each term carefully; 3(x − 4) gives 3x − 12, not 3x + 12.
- Writing 2(x + 5) = 2x + 5 instead of 2x + 10 → The multiplier acts on every term, including the constant.
- Thinking the distributive property only works with addition → It works equally with subtraction.
- Mixing up distribution with simple addition → 2 + (3 × 4) is not the same as (2 + 3) × (2 + 4); distribution applies when multiplication is outside the bracket.
Quick revision
- a × (b + c) = a × b + a × c distributes multiplication over addition.
- The same rule works for subtraction: a × (b − c) = a × b − a × c.
- Use distribution to make mental calculations easier by breaking numbers apart.
- When expanding brackets in algebra, multiply the outside term with every term inside.
- Factoring is the reverse: pull out a common factor to write a sum as a product.