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.
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Expand and simplify $2(x+3) + 3(x+2)$. Show every step.
Expand 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.
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
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!
Step 1: Expand every bracket. Step 2: Collect like terms.
When a bracket is subtracted, flip every sign inside after expanding.
Expand each bracket one at a time, then collect all like terms at the end.
| 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
- 1Expand the first bracket$2(3x-1) = 6x - 2$$2 \times 3x = 6x$ and $2 \times (-1) = -2$.
- 2Expand the second bracket$-3(x+4) = -3x - 12$$-3 \times x = -3x$ and $-3 \times 4 = -12$. Note the minus stays.
- 3Write the full expression$6x - 2 - 3x - 12$Combine both expansions. No brackets left.
- 4Collect like terms$x$-terms: $6x - 3x = 3x$. Constants: $-2 - 12 = -14$$6 - 3 = 3$. $-2 + (-12) = -14$.
- 5Final answer$3x - 14$Check: $x=1$. Original: $2(3-1)-3(1+4) = 4-15 = -11$. Answer: $3-14 = -11$ ✓
How are you completing this lesson?
Brain Trainer · 4 problems
1 Expand and simplify $2(x+3) + 3(x+1)$.
$2x+6+3x+3 =$ $5x+9$$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$
Show Your Working · 3 questions
Q6. Expand and simplify $3(x+2) + 2(x+1)$.
Q7. Expand and simplify $2(3x-1) - 3(x+4)$.
Q8. The perimeter of a triangle is $2(x+3) + 3(x+1) + (x-2)$. Simplify and find the perimeter when $x=2$.
Stretch. If $2(x+3) + k(x-1) = 7x+5$, find the value of $k$.
Two brackets and one sign trap
Two brackets and one sign trap. A student expands $2(3x+4)+3(x-2)$ and obtains $9x+14$.
Expand and simplify the original expression, showing the constant terms separately. Use $x=4$ to check your result and explain the student’s error.
Show your working first, then open the worked solution to check your reasoning.
Check the worked solution
Expand to $6x+8+3x-6$. Collecting like terms gives $9x+2$. The constant terms are $8-6=2$; multiplying $3(x-2)$ gives $3x-6$, not $3x+6$. At $x=4$, the original is $2(16)+3(2)=38$ and the simplified form gives $9(4)+2=38$. The student’s expression gives 50.
Key Concept
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Formulas
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Watch Out
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Check
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Practice
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Next
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Interactive: Algebra Machine
Substitute numbers into algebraic expressions and see them evaluate step by step.
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