Practice Combining Like Terms with Negative Coefficients and Distribution
| Site: | Saylor Academy |
| Course: | MA007: Algebra |
| Book: | Practice Combining Like Terms with Negative Coefficients and Distribution |
| Printed by: | Guest user |
| Date: | Tuesday, 15 July 2025, 7:37 AM |
Description
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buttons.Practice Problems
Learning mathematics is all about practicing mathematics. Now that you have successfully combined like terms, let's practice using the distributive property and then combine like terms all in one problem. If you need help, use the review tools at the bottom of the page.
- Simplify to create an equivalent expression.
\(2(-n-3)-7(5+2n)\)
Choose 1 answer:
- \(-16n-37\)
- \(-16n-41\)
- \(16n-41\)
- \(16n+41\)
- Simplify to create an equivalent expression.
\(-3z-(-z-2)\)
Choose 1 answer:
- \(-4z+2\)
- \(-2z-2\)
- \(-2z+2\)
- \(4z+2\)
- Simplify to create an equivalent expression.
\(-3(2+4k) + 7(2k-1)\)
Choose 1 answer:
- \(2k-13\)
- \(8k-13\)
- \(2k+13\)
- \(2k-7\)
- Simplify to create an equivalent expression.
\(2-4(5p+1)\)
Choose 1 answer:
- \(-20p-2\)
- \(-5p-4\)
- \(-20p+2\)
- \(-5p+4\)
Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:combine-like-terms/e/combining_like_terms_2
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
Answers
\(-16n-41\)
\(-2z+2\)
\(2k-13\)
\(-20p-2\)
Hints
- The simplified expression is \(-16n -41\).
- Distribute the 2 to each term inside the first set of parentheses:
- \(2(-n-3)-7(5+2n) = -2n -6 -7 (5+2n)\)
- Distribute the -7 to each term inside the second set of parentheses:
- \(-2n-6-7(5+2n) = -2n -6 -35 -14n\)
- Rewrite the expression to group the n-terms and numeric terms, and then combine like terms:
\(-2n-14n-6-35 = -16n -41\)
- Distribute the 2 to each term inside the first set of parentheses:
- The simplified expression is \(-2z+2\).
- The minus sign in front of the parentheses means we multiply each term inside the parentheses by -1:
- \(-3z-1(-z-2) = -3z+z+2\)
- Combine the z-terms:
\(-3z+z+2 = -2z+2\)
- The minus sign in front of the parentheses means we multiply each term inside the parentheses by -1:
- The simplified expression is \(2k-13\).
- Distribute the -3 to each term inside the first set of parentheses:
- \(-3(2+4k) + 7(2k-1) = -6-12k + 7(2k-1)\)
- Distribute the 7 to each term inside the second set of parentheses:
- \(-6-12k + 7(2k-1) = -6-12k+14k-7\)
- Rewrite the expression to group the k-terms and numeric terms, and then combine like terms:
\(-12k + 14k-6-7 = 2k-13\)
- Distribute the -3 to each term inside the first set of parentheses:
- The simplified expression is \(-20p-2\).
- Distribute the -4 to each term inside the parentheses:
- \(2-4(5p+1)=2-20p-4\)
- Combine the numeric terms:
- \(2-20p-4=-20p-2\)
- Distribute the -4 to each term inside the parentheses: