Negative Traps Worksheet
Pre-Algebra • Expressions • Skill 4.2
Negative Traps Worksheet
Distributive Property with Negative Signs & Combining Like Terms
Name:
Date: Period:
Worked Anchor Model Simplify: \(-2(3a - 4b) + (a + 2b)\)
Watch the Double Negative!
1 Distribute Multipliers
Multiply -2 across both inside terms:
\(-2 \times 3a = -6a\)
\(-2 \times (-4b) = \mathbf{+8b}\)
\(*(a+2b) = +1a + 2b\)
Trap: \(-2 \cdot -4 \neq -8\)
2 Group Like Terms
Write out all expanded terms and group by matching variable:
\(-6a + 8b + 1a + 2b\)
\(a\): \((-6a + 1a)\)
\(b\): \((+8b + 2b)\)
Remember: \(+a\) has coefficient \(+1\)
3 Combine & Simplify
Add coefficients of like terms to write the final simplified answer:
\(-6 + 1 = -5 \longrightarrow \mathbf{-5a}\)
\(8 + 2 = 10 \longrightarrow \mathbf{+10b}\)
\(-5a + 10b\)
3 Sign Rules to Remember:
• \((-)(-) = (+)\) • \((-)(+) = (-)\) • The sign in front stays glued to its term
A Guided Practice • Follow the 3 Steps
Show every expansion step clearly
1. Simplify: \(-3(2x - 5y) + (4x - y)\) Watch: \(-3 \times (-5y)\)
Expanded terms & grouping:
Final Answer:
2. Simplify: \(-4(m - 3n) - 2(2m + n)\) Both parentheses have negative multipliers
Expanded terms & grouping:
Final Answer:
3. Simplify: \(5(2p - q) - 3(p - 4q)\) Watch: \(-3 \times (-4q)\)
Expanded terms & grouping:
Final Answer:
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Independent Practice & Error Analysis
Apply your skills and spot common algebraic pitfalls
Target: 100% Sign Accuracy
B Independent Practice • Show All Work
4. \(-2(5k - 4m) + (3k + 7m)\)
Answer:
5. \(6(2u - v) - 3(4u - 5v)\)
Answer:
6. \(-(4x - 7y) + 3(2x - y)\) Notice the leading \(-\)
Answer:
7. \(-5(2a - b) + 4(a - 3b) - (a + b)\) 3 Parts
Answer:
C
Spot the Trap • Detective Challenge
Marcus attempted to simplify \(-2(3x - 5y) + (x - 4y)\) below, but made a classic sign error.
Marcus's Notebook:
\(-2(3x - 5y) + (x - 4y)\)
= -6x - 10y + x - 4y
= -5x - 14y ✗
Explain the mistake Marcus made in Line 1:
Correct Final Answer:
D
The Proof Check • Substitute & Verify
Verify our anchor problem: \(-2(3a - 4b) + (a + 2b) = -5a + 10b\)
1. Plug \(a = 2\) and \(b = 3\) into the Original:
\(-2(3(2) - 4(3)) + ((2) + 2(3))\)
Value =
2. Plug \(a = 2\) and \(b = 3\) into the Simplified:
\(-5(2) + 10(3)\)
Value =
Do both expressions yield the exact same numerical value? If yes, the algebraic equivalence is verified!
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