Lesson 9~30 minUnit 2 · Patterns & Algebra+90 XP
Expanding and Simplifying
$2(x+3) + 4(x-1)$. Expand both brackets, then collect like terms. Two skills in one problem — this is where algebra gets real.
Today's hook: $2(x+3) + 4(x-1)$. Expand both brackets. Then simplify. How many terms are in your final answer?
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Expand and simplify $2(x+3) + 3(x+2)$. Show every step.
Record in workbook.
1
The Big Idea
+5 XP to readExpand each bracket separately, then collect like terms. Two skills, one problem. Expand first, simplify second.
$2(x+3) + 4(x-1)$: expand to $2x+6+4x-4$, then collect: $6x+2$. Expand every bracket before combining.
$2(x+3) + 4(x-1) = 6x + 2$
Expand ALL first
Never collect terms before expanding. Complete expansion first.
Then collect like terms
After expanding, group and combine matching terms.
Track signs
$+4(x-1) = +4x-4$. The sign in front belongs to the bracket.
2
What You'll Master
objectives
Know
- How to expand multiple brackets
- That expansion comes before simplifying
- How signs affect each bracket
Understand
- Why we expand before collecting
- How subtraction changes bracket signs
- That the final answer should be fully simplified
Can Do
- Expand and simplify expressions with 2+ brackets
- Handle subtracted brackets
- Check answers by substitution
3
Words You Need
vocabulary
ExpandRemove brackets using the distributive law.
SimplifyCollect like terms after expanding. No brackets left.
Multiple BracketsTwo or more bracket groups. Expand each separately.
Subtracted BracketA bracket with a minus sign before it. Flip all signs inside.
Like TermsTerms with the same variable part. Combine after expanding.
Fully SimplifiedNo brackets, no like terms left to combine.
Wrong: $2(x+3) + 4(x-1) = 2x+3+4x-1 = 6x+2$
Right: $= 2x+6+4x-4 = 6x+2$. The 3 and 1 must ALSO be multiplied!
Wrong: $3(x+2) - (x-1) = 3x+6-x-1$
Right: $= 3x+6-x+1 = 2x+7$. Minus bracket flips ALL signs!
5
The Two-Step Method
+5 XPStep 1: Expand every bracket. Step 2: Collect like terms.
6
Subtracted Brackets
+5 XPWhen a bracket is subtracted, flip every sign inside after expanding.
Try It: $2(x+1) - 3(x-2)$.Ans: $2x+2-3x+6 = -x+8$
7
Three or More Brackets
+5 XPExpand each bracket one at a time, then collect all like terms at the end.
8
Quick Reference Table
+5 XP
| Expression | Expanded | Simplified |
|---|
| $2(x+3)+4(x-1)$ | $2x+6+4x-4$ | $6x+2$ |
| $3(x+2)-(x-1)$ | $3x+6-x+1$ | $2x+7$ |
| $2(x+1)+3(x+2)-(x-1)$ | $2x+2+3x+6-x+1$ | $4x+9$ |
Watch Me Solve It · Worked example
Watch Me Solve It · Full expansion
+15 XP per stepQ
PROBLEM
Expand and simplify $2(3x-1) - 3(x+4)$.
1
Expand the first bracket
$2(3x-1) = 6x - 2$
$2 \times 3x = 6x$ and $2 \times (-1) = -2$.
2
Expand the second bracket
$-3(x+4) = -3x - 12$
$-3 \times x = -3x$ and $-3 \times 4 = -12$. Note the minus stays.
3
Write the full expression
$6x - 2 - 3x - 12$
Combine both expansions. No brackets left.
4
Collect like terms
$x$-terms: $6x - 3x = 3x$. Constants: $-2 - 12 = -14$
$6 - 3 = 3$. $-2 + (-12) = -14$.
5
Final answer
$3x - 14$
Check: $x=1$. Original: $2(3-1)-3(1+4) = 4-15 = -11$. Answer: $3-14 = -11$ ✓
Nice work — XP earned
Answer$3x - 14$
$2(x+3)+4(x-1) = 2x+3+4x-1$
Didn't multiply the constants! 2 must multiply 3, 4 must multiply -1.
Fix: use arrows. Every term inside gets multiplied by the outside term.
$3(x+2)-(x-1) = 3x+6-x-1$
Forgot to flip signs for subtracted bracket. $-(x-1) = -x+1$ not $-x-1$.
Fix: minus bracket = flip ALL signs. Write it out: $-(x-1) = -x+1$.
Collecting before expanding
$2(x+3)+4(x-1) \\\ 6(x+3-1) = 6(x+2)$
Fix: expand first, collect second. Never collect across brackets!
How are you completing this lesson?
Brain Trainer · 4 problems
D
Brain Trainer · Mixed
4 problems
1 Expand and simplify $2(x+3) + 3(x+1)$.
$2x+6+3x+3 =$ $5x+9$$5x+9$
2 Expand and simplify $4(2x-1) - 2(x+3)$.
$8x-4-2x-6 =$ $6x-10$$6x-10$
3 Expand and simplify $3(x+2) - (x-1)$.
$3x+6-x+1 =$ $2x+7$$2x+7$
4 Expand and simplify $2(x+1) + 3(x-2) - (x+4)$.
$2x+2+3x-6-x-4 =$ $4x-8$$4x-8$
Complete in workbook.
$2(x+3) + 3(x+1) = $
$3(2x+1) - (x-2) = $
$2(x-1) + 3(x+2) - (x-3) = $
$4(2x-3) - 2(3x-1) = $
A student writes $2(x+3)+4(x-1) = 2x+3+4x-1$. What is the error?
Show Your Working · 3 questions
Show Your Working
9 marks total
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Medium
2 MARKS
Q6. Expand and simplify $3(x+2) + 2(x+1)$.
Answer in your workbook.
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Medium
3 MARKS
Q7. Expand and simplify $2(3x-1) - 3(x+4)$.
Answer in your workbook.
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Medium
4 MARKS
Q8. The perimeter of a triangle is $2(x+3) + 3(x+1) + (x-2)$. Simplify and find the perimeter when $x=2$.
Answer in your workbook.
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Hard
3 MARKS
Stretch. If $2(x+3) + k(x-1) = 7x+5$, find the value of $k$.
Answer in your workbook.
Stretch Challenge · +25 XP, +10 coins
Extension Problems
Ready for a bigger challenge? Try these extension problems.
Key Concept
Review the main ideas from this lesson.
Formulas
Key formulas and rules.
Watch Out
Common mistakes to avoid.
Check
Always verify your answers.
Practice
Keep practicing to master.
Next
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Interactive: Algebra Machine
Substitute numbers into algebraic expressions and see them evaluate step by step.
Mark lesson as complete
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