Like Terms Lab Slides
Algebra 1 Review
Concept Workshop
Algebraic Foundations
Like Terms Lab
Master term anatomy, spot matching variable parts, control negative signs, and simplify expressions with total confidence.
1
Term Anatomy
2
Worked Models
3
Class Challenges
Anatomy of an Algebraic Term
Concept 01
Dissecting the Term
- 7 x 3
Sign
Negative
Coefficient
7
Variable
x
Exponent
3
The Invisible 1
When you see \(x\), its coefficient is actually 1. When you see \(-x\), it is -1.
Constant Terms
A standalone number like +5 or -12 has no variable. Constants are like terms with each other!
Rule of Thumb: Terms are separated by addition (+) and subtraction (-) signs.
The Like Terms Matching Test
Concept 02
Like Terms
Must share the exact same variables with the exact same exponents.
\(4x\) and \(-9x\) Same: \(x^1\)
\(3m^2\) and \(10m^2\) Same: \(m^2\)
\(-8\) and \(15\) Constants
Coefficients CAN be different!
Unlike Terms
Different variables OR different exponents. Cannot be combined!
\(5x\) and \(5y\) Different letter
\(4x^2\) and \(4x^3\) Different power
\(7n\) and \(7\) Variable vs No Var
Do not blend these together!
Remember: Apples and oranges don't make "orapples." If exponents or variables differ, keep them separate!
The Golden Rule: Sign Ownership
Crucial Habit
The operation symbol (+ or -) directly in front of a term BELONGS to that term!
Always circle or box the sign together with the number!
Visual Box Strategy
\(6x\)
positive \(6x\)
\(- 8\)
negative \(8\)
\(+ 2x\)
positive \(2x\)
\(- 5\)
negative \(5\)
x-terms: \(6x + 2x = 8x\)
constants: \(-8 - 5 = -13\)
Combined Result: \(8x - 13\) (Never write \(8x + -13\))
Worked Model 1: Linear Terms & Constants
Step-by-Step
Original Expression
\(5k - 4 - 9k + 12\)
1
Identify Like Terms
Group terms sharing the same variable part.
\(k\)-family: \(5k\) and \(-9k\)
Constants: \(-4\) and \(+12\)
2
Combine Coefficients
Add or subtract the front numbers only.
\(5 - 9 = -4\) \(\rightarrow -4k\)
\(-4 + 12 = +8\)
3
Write Clean Answer
Standard form: variables first, constants last.
\(-4k + 8\)
Question for Class: Can we simplify \(-4k + 8\) into \(4k\)? No! One has \(k\), the other doesn't!
Worked Model 2: Exponent Sorting
Advanced Trap
Original Expression
\(4x^2 + 7x - x^2 - 10x + 6\)
\(x^2\) Terms Power: 2
\(4x^2\)
\(-1x^2\)
\(3x^2\)
\(x\) Terms Power: 1
\(+7x\)
\(-10x\)
\(-3x\)
Constants No Variable
\(+6\)
(Single term)
\(+6\)
Final Simplified Form:
\(3x^2 - 3x + 6\)
Notice: exponents never changed!
Active Practice: Whiteboards Ready
Your Turn
Problem A Single Variable
\(11y - 8 - 4y - 5\)
Step 1: Circle \(11y\) and \(-4y\)
Step 2: Box \(-8\) and \(-5\)
Solution: \(7y - 13\)
Problem B Two Variables
\(9a + 3b - 2a - 8b\)
Step 1: Combine \(9a - 2a = 7a\)
Step 2: Combine \(+3b - 8b = -5b\)
Solution: \(7a - 5b\)
Partner Check: Compare your signs! Did anyone accidentally get \(-8 - 5 = -3\)? Watch negative integers!
Trap Alerts & Quick Check
Wrap-Up
Trap 1: Exponent Blending
Adding exponents when combining.
\(2x + 3x \neq 5x^2\)
\(2x + 3x = 5x\)
Trap 2: Lost Negative
Leaving the sign behind.
\(4 - 7x \neq +7x\)
The term is \(-7x\)
Trap 3: Vanishing 1
Treating \(x\) as 0 instead of 1.
\(6x - x \neq 6\)
\(6x - 1x = 5x\)
Final Exit Challenge
Simplify: \(8x^2 - 3x + 4 - 5x^2 + 9x - 10\)
Target Solution \(3x^2 + 6x - 6\)
