Mathematics • Year 10 • Unit 2 • Lesson 2
Expanding Brackets — Skill Drill
Build fluency with the distributive law a(b + c) = ab + ac. Multiply the outside through every inner term — keep the signs straight, and watch the negative multiplier. One worked example, one guided trace, eight independent problems.
1. I do — fully worked example
This one features a negative multiplier — the most common place to drop a sign. Read every step.
Problem. Expand −2(3y − 4).
Step 1 — Identify the multiplier and inner terms.
Multiplier: −2. Inner terms: 3y and −4.
Reason: the multiplier is whatever sits outside the bracket — and it brings its sign with it.
Step 2 — Multiply the multiplier by each inner term, signs and all.
(−2) × (3y) + (−2) × (−4)
Reason: distributive law — every inner term gets multiplied by the outside.
Step 3 — Evaluate each product (mind the signs).
(−2)(3y) = −6y and (−2)(−4) = +8
Reason: negative × positive = negative; negative × negative = positive.
Step 4 — Write the expanded form.
= −6y + 8
Reason: there are no like terms to combine, so this is the simplest form.
Answer: −2(3y − 4) = −6y + 8.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank. 5 marks
Problem. Expand and simplify 3(x + 2) − 2(x − 4).
Step 1 — Expand the first bracket: 3(x + 2) = 3 × x + 3 × 2 = ____ + ____.
Step 2 — Expand the second bracket. The multiplier is −2 (the minus sign comes WITH the 2):
−2(x − 4) = (−2) × x + (−2) × (−4) = ____ + ____
Step 3 — Combine the two expansions:
3x + 6 + (____) + (____)
Step 4 — Collect like terms (x-group, then constants):
x-group: 3x + ____ = ____ x
constants: 6 + ____ = ____
Step 5 — Write the simplified expression:
Final answer = ____________________
3. You do — independent practice
Show your working. First four are foundation. Next two are standard (two brackets with simplification). Last two are extension.
Foundation — single bracket
3.1 Expand 4(x + 3). 1 mark
3.2 Expand 5(2x − 1). 1 mark
3.3 Expand −3(y + 4). 1 mark
3.4 Expand x(x + 5). 1 mark
Standard — expand AND simplify
3.5 Expand and simplify 5(2x − 3) + x. 2 marks
3.6 Expand and simplify 4(x + 1) − 3(x − 2). 2 marks
Extension — push your thinking
3.7 Expand and simplify 2x(3x − 4) + x(x + 5). 3 marks
3.8 A student writes 3(x + 4) = 3x + 4. In one sentence, say what the student forgot, then write the correct expansion. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (3(x + 2) − 2(x − 4))
Step 1: 3 × x + 3 × 2 = 3x + 6.
Step 2: −2(x − 4) = −2x + 8.
Step 3: 3x + 6 + (−2x) + (+8).
Step 4: x-group: 3x + (−2x) = 1x = x. Constants: 6 + 8 = 14.
Step 5: x + 14.
3.1 — 4(x + 3)
= 4(x) + 4(3) = 4x + 12.
3.2 — 5(2x − 1)
= 5(2x) + 5(−1) = 10x − 5.
3.3 — −3(y + 4)
= (−3)(y) + (−3)(4) = −3y − 12.
Negative multiplier hits BOTH inner terms.
3.4 — x(x + 5)
= x · x + x · 5 = x² + 5x.
x × x = x², not 2x.
3.5 — 5(2x − 3) + x
= 10x − 15 + x = 11x − 15.
3.6 — 4(x + 1) − 3(x − 2)
= 4x + 4 + (−3x + 6) = (4x − 3x) + (4 + 6) = x + 10.
The −3 multiplier turns −2 into +6 — two negatives make a positive.
3.7 — 2x(3x − 4) + x(x + 5)
2x(3x − 4) = 6x² − 8x.
x(x + 5) = x² + 5x.
Combine: (6x² + x²) + (−8x + 5x) = 7x² − 3x.
3.8 — The student forgot what?
The student only multiplied the 3 by the x and forgot to multiply it by the 4 — the multiplier must hit every inner term.
Correct expansion: 3(x + 4) = 3x + 12.