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).

Multiply the outside −3 by each inside term: −3 × 2x = −6x and −3 × −4 = +12.

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.)