To solve the problem of combining like terms, we need to group and simplify terms that have the same variable(s) and exponent(s). Let's go through each expression step by step.
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Expression 1: \( 8x + 3y - x - 2y \)
- Combine the \( x \)-terms: \( 8x - x = 7x \)
- Combine the \( y \)-terms: \( 3y - 2y = y \)
Simplified: \( 7x + y \)
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Expression 2: \( 3n + 7n - 2n + x + 8x \)
- Combine the \( n \)-terms: \( 3n + 7n - 2n = 8n \)
- Combine the \( x \)-terms: \( x + 8x = 9x \)
Simplified: \( 8n + 9x \)
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Expression 3: \( 2r - 5n + 9y - 3r + n \)
- Combine the \( r \)-terms: \( 2r - 3r = -r \)
- Combine the \( n \)-terms: \( -5n + n = -4n \)
- The \( y \)-term remains as it is: \( 9y \)
Simplified: \( -r - 4n + 9y \)
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Expression 4: \( 12y - 6x + 5y - 3x \)
- Combine the \( y \)-terms: \( 12y + 5y = 17y \)
- Combine the \( x \)-terms: \( -6x - 3x = -9x \)
Simplified: \( 17y - 9x \)
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Expression 5: \( -13n + 4n - r \)
- Combine the \( n \)-terms: \( -13n + 4n = -9n \)
- The \( r \)-term remains as it is: \( -r \)
Simplified: \( -9n - r \)
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Expression 6: \( 7xy - 8x + 6xy - y \)
- Combine the \( xy \)-terms: \( 7xy + 6xy = 13xy \)
- Combine the \( x \)-terms: \( -8x \) (no other \( x \)-terms)
- The \( y \)-term remains as it is: \( -y \)
Simplified: \( 13xy - 8x - y \)
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Expression 7: \( -14r - 10n - 3r - 9n \)
- Combine the \( r \)-terms: \( -14r - 3r = -17r \)
- Combine the \( n \)-terms: \( -10n - 9n = -19n \)
Simplified: \( -17r - 19n \)
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Expression 8: \( 6r + 9r - 2r - 13 \)
- Combine the \( r \)-terms: \( 6r + 9r - 2r = 13r \)
- The constant term remains as it is: \( -13 \)
Simplified: \( 13r - 13 \)
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Expression 9: \( n + r + x - 3x + 4r \)
- Combine the \( n \)-terms: \( n \) (no other \( n \)-terms)
- Combine the \( r \)-terms: \( r + 4r = 5r \)
- Combine the \( x \)-terms: \( x - 3x = -2x \)
Simplified: \( n + 5r - 2x \)
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Expression 10: \( 15y - 7x + 9z + 4z - 3x \)
- Combine the \( y \)-terms: \( 15y \) (no other \( y \)-terms)
- Combine the \( x \)-terms: \( -7x - 3x = -10x \)
- Combine the \( z \)-terms: \( 9z + 4z = 13z \)
Simplified: \( 15y - 10x + 13z \)
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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. \( 13r - 13 \)
9. \( n + 5r - 2x \)
10. \( 15y - 10x + 13z \)
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Boxed Final Answer:
\[
\boxed{
\begin{aligned}
1. & \ 7x + y \\
2. & \ 8n + 9x \\
3. & \ -r - 4n + 9y \\
4. & \ 17y - 9x \\
5. & \ -9n - r \\
6. & \ 13xy - 8x - y \\
7. & \ -17r - 19n \\
8. & \ 13r - 13 \\
9. & \ n + 5r - 2x \\
10. & \ 15y - 10x + 13z
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of math worksheet combining like terms.
