Term Fusion Notes Handout
8th Grade Math Expressions & Equations
TERM FUSION // GUIDED NOTES
Mastering the Art of Combining Like Terms
Name:
Date: Period:
1
Anatomy of an Algebraic Expression
Expression Breakdown
-7x2 + 9
Coefficient
Variable
Exponent
Constant
• Term: A single number, variable, or numbers and variables multiplied together, separated by signs.
• Coefficient: The numerical factor multiplied by a variable. If no number is visible, the coefficient is !
• Variable: A symbol (usually a letter) that represents an quantity.
• Constant: A fixed value with variables attached.
2
The "Like Terms" Identification Rule
Golden Rule: Two or more terms are LIKE TERMS if and only if they have:
A The EXACT SAME
B Raised to the EXACT SAME
| Pair of Terms | Like or Unlike? | Reason / Analysis |
|---|
| \( 4x \) & \( -9x \) | LIKE | Both have variable \(x\) with exponent 1. |
| \( 3y^2 \) & \( 5y^2 \) | LIKE | Both have variable \(y\) raised to power 2. |
| \( 7a \) & \( 7b \) | UNLIKE | Different variables (\(a\) vs. \(b\)), even with equal coefficients! |
| \( 6m^3 \) & \( 6m \) | Like / Unlike? | Different exponents: |
| \( -14 \) & \( 8 \) | Like / Unlike? | Both are (no variables attached). |
3
How to Combine Like Terms
Step 1: Combine Coefficients
Add or subtract ONLY the of the like terms.
Step 2: Keep Variables Untouched
Keep the and exponent exactly the SAME! Never add exponents!
Example A
\( 5x + 3x \)
\(= (5 + 3)x\)
=
Example B
\( 8y - 11y \)
\(= (8 - 11)y\)
=
Example C (Hidden 1)
\( 7m - m \)
\(= (7 - 1)m\)
=
Example D (Negatives)
\( -4k - 6k \)
\(= (-4 - 6)k\)
=
Pro Tip: Constants (\(-3, 8, 15\)) can always be combined with each other!
Page 1 of 2
STRATEGY & MULTI-TERM SIMPLIFICATION
Combining like terms across multi-term expressions
Page 2 // Practice & Mastery
4
The "Shape & Sign" Visual Strategy
Crucial Rule!
ALWAYS include the SIGN (+ or -) immediately in front of each term inside your shape!
Model Example:
6x + 4 - 2x - 9
➔
Group terms: (6x - 2x) + (4 - 9)
➔
4x - 5
Box like term family 1 (with signs)
Circle like term family 2 (with signs)
5
Guided Practice (Draw Shapes First!)
1. Two Variables Difficulty: ★☆☆
\( 8a + 5b + 3a - 2b \)
Group \(a\)'s: | Group \(b\)'s:
Final Answer:
2. Exponents Included Difficulty: ★★☆
\( 4x^2 + 7x - 3x^2 + 2x \)
Group \(x^2\): | Group \(x\):
Final Answer:
3. Variable & Constants Difficulty: ★★☆
\( 12 - 5w + 8 - w \)
Watch out: \(-w = -1w\)!
Final Answer:
4. Multi-Term Mix Difficulty: ★★★
\( -3y + 9 - 4y - 15 + 2y \)
Group \(y\)'s: | Constants:
Final Answer:
3 Traps to Avoid (Error Analysis)
Trap 1: The Exponent Trap
\( 3x + 2x \neq 5x^2 \)
Do NOT add exponents! Keep variable the same.
Correct:
Trap 2: The Invisible One
\( 6y - y \neq 6 \)
\( -y \) actually means .
Correct:
Trap 3: Sign Left Behind
\( 5 - 8x \)
The minus belongs to , NOT the 5!
Sign of \(8x\):
Mastery Check (Simplify Completely)
Show All Work
A. \( 9c + 4 - 2c + 7 \)
=
B. \( -5p + 3q - p - 8q \)
=
C. \( 8x^2 + 6x - 2x^2 - 6x \)
=
Grade 8 Mathematics • Algebraic Expressions No Distributive Property • Pure Term Combination Page 2 of 2
