One rule does an enormous amount of work in algebra: a(b + c) = ab + ac. Multiply what is outside by everything inside.
Study Zone is free for our students — you just need to log in with your WhatsApp number first.
Log in with WhatsApp →The first two chapters of every book are free once you're logged in. To open this one, request an unlock and we'll get back to you on WhatsApp.
Think of 6 × 23 as 6 × (20 + 3) = 120 + 18 = 138. You already do this in your head — algebra just names it.
📦 Multiply the outside by every inside term
a(b + c) = ab + ac. Nothing inside may be skipped.
a(b − c) = ab − ac. The minus sign travels with the term.
A negative outside flips every sign inside: −2(x − 3) = −2x + 6.
The commonest mistake in Class 8. −2(x − 3) is −2x + 6, not −2x − 6. Multiplying two negatives gives a plus. Write the sign before you write the number.
When both parts have two terms, every term in the first must meet every term in the second — four products in all.
🔗 Watch it work
| Problem | Four products | Answer |
|---|---|---|
| (x+2)(x+3) | x² + 3x + 2x + 6 | x² + 5x + 6 |
| (x+5)(x−2) | x² − 2x + 5x − 10 | x² + 3x − 10 |
| (2x+1)(x+4) | 2x² + 8x + x + 4 | 2x² + 9x + 4 |
Only like terms combine. 3x and 2x add to 5x, but x² and 5x cannot be added — they are different kinds of term, just as 3 apples and 5 oranges stay separate.
These three come up constantly. Learning them saves you the four-product working every time.
⭐ Learn all three
| Identity | Example |
|---|---|
| (a + b)² = a² + 2ab + b² | (x+3)² = x² + 6x + 9 |
| (a − b)² = a² − 2ab + b² | (x−4)² = x² − 8x + 16 |
| (a + b)(a − b) = a² − b² | (x+5)(x−5) = x² − 25 |
(a + b)² is NOT a² + b². The middle term 2ab is the one everybody forgets. Check with numbers: (2+3)² = 25, but 2² + 3² = 13. They are not the same.
12 questions on expanding and multiplying. Multiply every term. 🍀
