Let's solve each expression by
combining like terms. Like terms are terms that have the same variables raised to the same powers. We can add or subtract their coefficients.
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1. $ 8x + 3y - x - 2y $
- Combine $ 8x - x = 7x $
- Combine $ 3y - 2y = y $
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Answer: $ 7x + y $
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2. $ 3n + 7n - 2n + x + 8x $
- Combine $ 3n + 7n - 2n = 8n $
- Combine $ x + 8x = 9x $
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Answer: $ 8n + 9x $
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3. $ 2r - 5n + 9y - 3r + n $
- Combine $ 2r - 3r = -r $
- Combine $ -5n + n = -4n $
- $ 9y $ stays
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Answer: $ -r - 4n + 9y $
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4. $ 12y - 6x + 5y - 3x $
- Combine $ 12y + 5y = 17y $
- Combine $ -6x - 3x = -9x $
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Answer: $ 17y - 9x $
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5. $ -13n + 4n - r $
- Combine $ -13n + 4n = -9n $
- $ -r $ stays
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Answer: $ -9n - r $
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6. $ 7xy - 8x + 6xy - y $
- Combine $ 7xy + 6xy = 13xy $
- $ -8x $ stays
- $ -y $ stays
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Answer: $ 13xy - 8x - y $
> Note: $ xy $ and $ x $, $ y $ are not like terms, so they cannot be combined.
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7. $ -14r - 10n - 3r - 9n $
- Combine $ -14r - 3r = -17r $
- Combine $ -10n - 9n = -19n $
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Answer: $ -17r - 19n $
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8. $ 6r + 9r - 2r - 13n $
- Combine $ 6r + 9r - 2r = 13r $
- $ -13n $ stays
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Answer: $ 13r - 13n $
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9. $ n + r + x - 3x + 4r $
- Combine $ n $ → stays
- Combine $ r + 4r = 5r $
- Combine $ x - 3x = -2x $
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Answer: $ n + 5r - 2x $
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10. $ 15y - 7x + 9z + 4z - 3x $
- Combine $ -7x - 3x = -10x $
- Combine $ 9z + 4z = 13z $
- $ 15y $ stays
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Answer: $ 15y - 10x + 13z $
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✔ Final Answers:
1. $ 7x + y $
2. $ 8n + 9x $
3. $ -r - 4n + 9y $
4. $ 17y - 9x $
5. $ -9n - r $
6. $ 13xy - 8x - y $
7. $ -17r - 19n $
8. $ 13r - 13n $
9. $ n + 5r - 2x $
10. $ 15y - 10x + 13z $
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✔ Tip: Always group like terms together before combining coefficients. Remember that constants (numbers without variables) are also like terms with each other.
Let me know if you'd like this as a printable worksheet!
Parent Tip: Review the logic above to help your child master the concept of combining like terms worksheet 8th grade.
