Simplifying algebraic expressions makes them shorter and easier to work with. You'll combine like terms, use the distributive property, and clean up expressions to their simplest form!
What Does "Simplify" Mean?
To simplify an expression means to make it as short and clean as possible by:
Combining like terms
Using the distributive property
Removing parentheses
Writing in standard form
Example:
Before: 3x + 2x + 5 - 2
After: 5x + 3
Both expressions are equal, but the simplified version is cleaner!
Like Terms
Like terms have the SAME variable raised to the SAME power.
How can I study Simplifying Expressions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 5 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
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Yes — all study notes, flashcards, and practice problems for Simplifying Expressions on Study Mondo are 100% free. No account is needed to access the content.
What course covers Simplifying Expressions?▾
Simplifying Expressions is part of the Grade 7 Math course on Study Mondo, specifically in the Expressions and Equations section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Simplifying Expressions?
3x and 5y (different variables)
4x and 4x² (different exponents)
2xy and 3x (different variables)
Why it matters: You can only combine like terms!
Combining Like Terms
Add or subtract the coefficients, keep the variable part the same.
Example 1: Simple Addition
Simplify: 4x + 7x
Solution:
Both terms have x
Add coefficients: 4 + 7 = 11
Keep the variable: x
Answer: 11x
Think: 4 apples + 7 apples = 11 apples
Example 2: With Subtraction
Simplify: 9y - 3y
Solution:
Both terms have y
Subtract coefficients: 9 - 3 = 6
Answer: 6y
Example 3: Multiple Terms
Simplify: 5x + 3x - 2x
Solution:
All terms have x
Combine: 5 + 3 - 2 = 6
Answer: 6x
Example 4: With Constants
Simplify: 3x + 7 + 2x - 4
Solution:Step 1: Group like terms
x terms: 3x + 2x
Constants: 7 - 4
Step 2: Combine each group
3x + 2x = 5x
7 - 4 = 3
Step 3: Write final answer
Answer: 5x + 3
Example 5: Negative Coefficients
Simplify: 8a - 5a + 3a
Solution:
All have variable a
Combine: 8 - 5 + 3 = 6
Answer: 6a
The Distributive Property
Formula: a(b + c) = ab + ac
Multiply the number outside the parentheses by EACH term inside.
Example 1: Basic Distribution
Simplify: 3(x + 4)
Solution:
3 × x = 3x
3 × 4 = 12
Answer: 3x + 12
Example 2: Negative Distribution
Simplify: -2(y - 5)
Solution:
-2 × y = -2y
-2 × (-5) = +10
Answer: -2y + 10
Important: Distribute the negative sign too!
Example 3: Variable Outside
Simplify: x(3 + 5)
Solution:
x × 3 = 3x
x × 5 = 5x
Answer: 3x + 5x = 8x
Example 4: Distribution with Three Terms
Simplify: 4(2x - 3 + y)
Solution:
4 × 2x = 8x
4 × (-3) = -12
4 × y = 4y
Answer: 8x - 12 + 4y
Combining Distribution and Like Terms
Many problems require both steps!
Example 1: Distribute Then Combine
Simplify: 2(x + 3) + 5x
Step 1: Distribute
2(x + 3) = 2x + 6
Step 2: Rewrite
2x + 6 + 5x
Step 3: Combine like terms
x terms: 2x + 5x = 7x
Constants: 6
Answer: 7x + 6
Example 2: Multiple Distributions
Simplify: 3(x + 2) + 4(x - 1)
Step 1: Distribute first parentheses
3(x + 2) = 3x + 6
Step 2: Distribute second parentheses
4(x - 1) = 4x - 4
Step 3: Rewrite
3x + 6 + 4x - 4
Step 4: Combine like terms
x terms: 3x + 4x = 7x
Constants: 6 - 4 = 2
Answer: 7x + 2
Example 3: With Negative Distribution
Simplify: 5(2y + 1) - 3(y - 4)
Step 1: Distribute
5(2y + 1) = 10y + 5
-3(y - 4) = -3y + 12 (watch the signs!)
Step 2: Rewrite
10y + 5 - 3y + 12
Step 3: Combine
y terms: 10y - 3y = 7y
Constants: 5 + 12 = 17
Answer: 7y + 17
Removing Parentheses
Positive Sign Before Parentheses
Just remove the parentheses - nothing changes!
Example: 3x + (2x + 5) = 3x + 2x + 5 = 5x + 5
Negative Sign Before Parentheses
Change the sign of EVERY term inside!
Example 1: 4x - (2x + 3)
Remove parentheses: 4x - 2x - 3
Combine: 2x - 3
Example 2: 7y - (3y - 5)
Remove parentheses: 7y - 3y + 5
Combine: 4y + 5
Think of it as: -(2x + 3) = -1(2x + 3) = -2x - 3
Simplifying with Multiple Variables
Combine terms with the same variable!
Example 1: Two Variables
Simplify: 3x + 2y + 5x - y
Solution:
x terms: 3x + 5x = 8x
y terms: 2y - y = y
Answer: 8x + y
Example 2: Three Variables
Simplify: 4a + 3b - 2a + 5c - b
Solution:
a terms: 4a - 2a = 2a
b terms: 3b - b = 2b
c terms: 5c
Answer: 2a + 2b + 5c
Simplifying with Exponents
Remember: Only combine terms with the same variable AND same exponent!
Example 1: Same Exponents
Simplify: 5x² + 3x² - 2x²
Solution:
All have x²
Combine: 5 + 3 - 2 = 6
Answer: 6x²
Example 2: Different Exponents
Simplify: 4x² + 3x + 2x² - x
Solution:
x² terms: 4x² + 2x² = 6x²
x terms: 3x - x = 2x
Answer: 6x² + 2x
Cannot combine x² and x - they're unlike terms!
Example 3: Mixed Variables and Exponents
Simplify: 2xy + 3x + xy - 5x
Solution:
xy terms: 2xy + xy = 3xy
x terms: 3x - 5x = -2x
Answer: 3xy - 2x
Order of Operations in Simplifying
Follow PEMDAS when simplifying!
Example: Simplify: 2(3x + 4) - 5 + 3x
Step 1: Parentheses/Distribution first
2(3x + 4) = 6x + 8
Step 2: Rewrite
6x + 8 - 5 + 3x
Step 3: Combine like terms
x terms: 6x + 3x = 9x
Constants: 8 - 5 = 3
Answer: 9x + 3
Real-World Applications
Perimeter Problems
Problem: A rectangle has length (3x + 2) and width (x + 5). Write a simplified expression for the perimeter.
Solution:
Perimeter = 2(length) + 2(width)
P = 2(3x + 2) + 2(x + 5)
P = 6x + 4 + 2x + 10
P = 8x + 14
Answer: Perimeter = 8x + 14
Shopping
Problem: You buy 3 shirts at xeachand2pairsofpantsaty each. Then you return 1 shirt. Write a simplified expression for the total cost.
Solution:
Total = 3x + 2y - x
Total = 2x + 2y
Answer: 2x + 2y
Common Mistakes to Avoid
❌ Mistake 1: Combining unlike terms
Wrong: 3x + 4y = 7xy
Right: 3x + 4y (cannot combine - different variables!)
❌ Mistake 2: Forgetting to distribute negative
Wrong: 5 - (x + 3) = 5 - x + 3 = 8 - x
Right: 5 - (x + 3) = 5 - x - 3 = 2 - x
❌ Mistake 3: Distributing to only one term
Wrong: 2(x + 3) = 2x + 3
Right: 2(x + 3) = 2x + 6
❌ Mistake 4: Combining different exponents
Wrong: 2x² + 3x = 5x³
Right: 2x² + 3x (cannot combine!)
❌ Mistake 5: Sign errors
Wrong: 4x - 2x = 2x or -2x? (confusion)
Right: 4x - 2x = 2x (4 minus 2 is positive 2)
Practice Strategy
Step 1: Look for parentheses
Distribute first!
Remove negative signs carefully
Step 2: Identify like terms
Circle or underline terms with the same variable/exponent
Step 3: Combine
Add/subtract coefficients
Keep variable parts the same
Step 4: Write in standard form
Usually highest exponent first
Then lower exponents
Then constants
Step 5: Check
Can you combine anything else?
Are all like terms together?
Standard Form
Standard form for polynomials: Write terms in descending order of exponents.
Example: Simplify and write in standard form: 5 + 3x² - 2x + x²
Step 1: Combine like terms
x² terms: 3x² + x² = 4x²
x terms: -2x
Constants: 5
Step 2: Write in standard form (highest exponent first)
Answer: 4x² - 2x + 5
Quick Tips
Tip 1: Like terms are "friends" - they can combine!
3x and 5x are friends → 8x
3x and 5y are NOT friends → stay separate
Tip 2: Distribute carefully with negatives
-(3x - 2) means multiply EVERYTHING by -1
Result: -3x + 2
Tip 3: Use different colors for different variables
Circle all x terms in blue
Circle all y terms in red
Makes it easy to see what combines!
Tip 4: Check by substituting a number
Original: 2(x + 3) + 4x
Simplified: 6x + 6
Test with x = 1: 2(1+3) + 4(1) = 2(4) + 4 = 12 ✓
Check: 6(1) + 6 = 12 ✓
Summary
Simplifying expressions means making them as short as possible by:
Using distributive property: a(b + c) = ab + ac
Combining like terms: Terms with same variable and exponent
Removing parentheses: Watch for negative signs!
Writing in standard form: Highest exponent first
Key Rules:
Only like terms can combine
Distribute to EVERY term inside parentheses
Negative before parentheses changes ALL signs inside
Different variables or exponents = unlike terms
Mastering simplification is essential for solving equations, factoring, and all of algebra!
Step 3: Combine like terms
x terms: -6x + 5x = -x
Constants: 12 + 5 - 7 = 10
Answer: -x + 10
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Yes, this page includes 5 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.