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 ✓.