Mathematics • Year 7 • Unit 2 • Lesson 9
Expanding and Simplifying
Build the basics: when you see two (or more) brackets being added or subtracted, expand each bracket fully FIRST, then collect like terms to simplify. Watch out for subtracted brackets — every sign inside flips.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Expand and simplify 2(3x − 1) − 3(x + 4).
Step 1 — Expand the first bracket.
2(3x − 1) = 2 × 3x + 2 × (−1) = 6x − 2
Reason: distributive law. The 2 outside multiplies BOTH the 3x and the −1.
Step 2 — Expand the second bracket (watch the minus sign in front!).
−3(x + 4) = −3 × x + (−3) × 4 = −3x − 12
Reason: the multiplier is −3 (negative). −3 × x = −3x, and −3 × 4 = −12.
Step 3 — Write the full expanded expression.
6x − 2 − 3x − 12
Reason: combine both expansions. No brackets left.
Step 4 — Collect like terms.
x-terms: 6x − 3x = 3x | constants: −2 − 12 = −14
Reason: like terms have the same letter part (or none). Group them and combine.
Answer: 2(3x − 1) − 3(x + 4) = 3x − 14. Check x = 1: original 2(3 − 1) − 3(1 + 4) = 4 − 15 = −11. Expanded 3 − 14 = −11 ✓.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Expand and simplify 3(x + 2) + 2(x + 1).
Step 1 — Expand the first bracket:
3(x + 2) = ______ + ______ = ______________
Step 2 — Expand the second bracket:
2(x + 1) = ______ + ______ = ______________
Step 3 — Write the full expanded expression:
____________________________________
Step 4 — Collect like terms:
x-terms: ______ + ______ = ______ | constants: ______ + ______ = ______. Final answer: ______________
3. You do — independent practice
Show your working under each question. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 Expand and simplify 2(x + 1) + 3(x + 4). 1 mark
3.2 Expand and simplify 4(x + 2) + 2(x + 3). 1 mark
3.3 Expand and simplify 3(x − 1) + 2(x + 5). 1 mark
3.4 Expand and simplify 5(x + 2) − (x + 3). (Note: the −1 multiplier in front of (x + 3) flips the signs.) 1 mark
Standard — combine two ideas
3.5 Expand and simplify 4(2x − 1) − 2(x + 3). 2 marks
3.6 Expand and simplify 3(x + 2) − (x − 1). 2 marks
Extension — push your thinking
3.7 Expand and simplify 2(x + 1) + 3(x − 2) − (x + 4). (Three brackets, one negative.) 3 marks
3.8 Expand and simplify 2(3x − 1) − 3(x + 4), then check by substituting x = 2 into both the original and your simplified answer. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (3(x + 2) + 2(x + 1))
Step 1: 3(x + 2) = 3x + 6.
Step 2: 2(x + 1) = 2x + 2.
Step 3: 3x + 6 + 2x + 2.
Step 4: x-terms: 3x + 2x = 5x. Constants: 6 + 2 = 8. Final answer: 5x + 8.
3.1 — 2(x + 1) + 3(x + 4)
Expanded: 2x + 2 + 3x + 12. Collected: 5x + 14.
3.2 — 4(x + 2) + 2(x + 3)
Expanded: 4x + 8 + 2x + 6. Collected: 6x + 14.
3.3 — 3(x − 1) + 2(x + 5)
Expanded: 3x − 3 + 2x + 10. Collected: 5x + 7.
3.4 — 5(x + 2) − (x + 3)
Expanded: 5x + 10 − x − 3 (the −1 flips both inside signs: −x − 3). Collected: 4x + 7.
3.5 — 4(2x − 1) − 2(x + 3)
Expanded: 8x − 4 − 2x − 6. Collected: x-terms 8x − 2x = 6x; constants −4 − 6 = −10. Answer: 6x − 10.
3.6 — 3(x + 2) − (x − 1)
Expanded: 3x + 6 − x + 1 (the −1 flips signs: −(x − 1) = −x + 1). Collected: 2x + 7.
3.7 — 2(x + 1) + 3(x − 2) − (x + 4)
Expanded: 2x + 2 + 3x − 6 − x − 4. Collected: x-terms 2x + 3x − x = 4x; constants 2 − 6 − 4 = −8. Answer: 4x − 8.
3.8 — 2(3x − 1) − 3(x + 4)
Expanded: 6x − 2 − 3x − 12. Collected: x-terms 6x − 3x = 3x; constants −2 − 12 = −14. Answer: 3x − 14.
Check with x = 2: Original 2(6 − 1) − 3(2 + 4) = 2 × 5 − 3 × 6 = 10 − 18 = −8. Simplified 3 × 2 − 14 = 6 − 14 = −8 ✓.