Mathematics • Year 7 • Unit 2 • Lesson 8

Expanding Single Brackets

Build the basics: use the distributive law a(b + c) = ab + ac to multiply the outside term by EVERY term inside the bracket. Use the arrow method, track signs carefully, and check by substituting a number.

Build · I Do / We Do / You Do

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 −3(2x − 4).

Step 1 — Identify the multiplier and the inside terms.

Multiplier: −3 | Inside: 2x and −4

Reason: the bracket has two terms, +2x and −4. The sign in front of each inside term belongs to that term.

Step 2 — Multiply the outside term by the first inside term.

−3 × 2x = −6x

Reason: neg × pos = neg. 3 × 2 = 6. So −6x.

Step 3 — Multiply the outside term by the second inside term.

−3 × (−4) = +12

Reason: neg × neg = POS! This is the step everyone trips on. 3 × 4 = 12, and the two negatives cancel.

Step 4 — Combine the two pieces.

−6x + 12

Check by substituting x = 1: original −3(2 − 4) = −3 × (−2) = 6. Expanded: −6 + 12 = 6 ✓.

Answer: −3(2x − 4) = −6x + 12.

Stuck? Revisit lesson § "The Distributive Law" — the outside term visits every inside term.

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 3(2x − 5).

Step 1 — Identify the multiplier and inside terms:

Multiplier = ______ | Inside terms = ______ and ______

Step 2 — Multiply the outside by the first inside term:

______ × ______ = ______

Step 3 — Multiply the outside by the second inside term (watch the −!):

______ × ______ = ______

Step 4 — Combine:

Final answer = ______________

Stuck? Revisit lesson § "Spot the Trap" — the sign in front of an inside term BELONGS to that term. Don't drop the minus.

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 4(x + 3). 1 mark

3.2 Expand 5(2x + 1). 1 mark

3.3 Expand 2(x − 6). 1 mark

3.4 Expand 7(a + 2). 1 mark

Standard — combine two ideas

3.5 Expand 3(2x − 5). (Watch the minus inside.) 2 marks

3.6 Expand −4(x + 3). (The negative outside changes every sign inside.) 2 marks

Extension — push your thinking

3.7 Expand −2(3x − 5). (Both signs are negative — what happens to the −5?) 3 marks

3.8 Expand x(x + 4). (The outside term is x — same letter as inside. Remember x × x = x².) 3 marks

Stuck on 3.8? x × x = x² (NOT 2x). x × 4 = 4x. Combine to get x² + 4x.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do (3(2x − 5))

Step 1: Multiplier = 3. Inside terms = 2x and −5.
Step 2: 3 × 2x = 6x.
Step 3: 3 × (−5) = −15.
Step 4: Final answer = 6x − 15.

3.1 — 4(x + 3)

4 × x = 4x. 4 × 3 = 12. Answer: 4x + 12.

3.2 — 5(2x + 1)

5 × 2x = 10x. 5 × 1 = 5. Answer: 10x + 5.

3.3 — 2(x − 6)

2 × x = 2x. 2 × (−6) = −12. Answer: 2x − 12.

3.4 — 7(a + 2)

7 × a = 7a. 7 × 2 = 14. Answer: 7a + 14.

3.5 — 3(2x − 5)

3 × 2x = 6x. 3 × (−5) = −15. Answer: 6x − 15.

3.6 — −4(x + 3)

−4 × x = −4x. −4 × 3 = −12 (neg × pos = neg). Answer: −4x − 12.

3.7 — −2(3x − 5)

−2 × 3x = −6x. −2 × (−5) = +10 (neg × neg = pos!). Answer: −6x + 10. Check x = 1: −2(3 − 5) = −2(−2) = 4, and −6 + 10 = 4 ✓.

3.8 — x(x + 4)

x × x = x². x × 4 = 4x. Answer: x² + 4x. (Not 5x — x times x is x², not 2x.)