To solve the problem of collecting like terms and simplifying the given expressions, we need to group together terms that have the same variable and then combine their coefficients. Let's go through each expression step by step.
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1) \( 7a + 10b + 6a - 3b \)
- Group the \( a \)-terms: \( 7a + 6a = 13a \)
- Group the \( b \)-terms: \( 10b - 3b = 7b \)
- Combine the results: \( 13a + 7b \)
Answer: \( 13a + 7b \)
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2) \( 10c + 9v + 6c - 7v \)
- Group the \( c \)-terms: \( 10c + 6c = 16c \)
- Group the \( v \)-terms: \( 9v - 7v = 2v \)
- Combine the results: \( 16c + 2v \)
Answer: \( 16c + 2v \)
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3) \( 8s + 4r + 13s + 6r \)
- Group the \( s \)-terms: \( 8s + 13s = 21s \)
- Group the \( r \)-terms: \( 4r + 6r = 10r \)
- Combine the results: \( 21s + 10r \)
Answer: \( 21s + 10r \)
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4) \( 4d + 6e - 5d + 4e \)
- Group the \( d \)-terms: \( 4d - 5d = -d \)
- Group the \( e \)-terms: \( 6e + 4e = 10e \)
- Combine the results: \( -d + 10e \)
Answer: \( -d + 10e \)
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5) \( 13f + 7g + 3f + 4g \)
- Group the \( f \)-terms: \( 13f + 3f = 16f \)
- Group the \( g \)-terms: \( 7g + 4g = 11g \)
- Combine the results: \( 16f + 11g \)
Answer: \( 16f + 11g \)
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6) \( 9p - 13q + 12p + 19q \)
- Group the \( p \)-terms: \( 9p + 12p = 21p \)
- Group the \( q \)-terms: \( -13q + 19q = 6q \)
- Combine the results: \( 21p + 6q \)
Answer: \( 21p + 6q \)
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7) \( 2b + 9c + 4b - 6c \)
- Group the \( b \)-terms: \( 2b + 4b = 6b \)
- Group the \( c \)-terms: \( 9c - 6c = 3c \)
- Combine the results: \( 6b + 3c \)
Answer: \( 6b + 3c \)
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8) \( 5k + 14m + 4k + 12m \)
- Group the \( k \)-terms: \( 5k + 4k = 9k \)
- Group the \( m \)-terms: \( 14m + 12m = 26m \)
- Combine the results: \( 9k + 26m \)
Answer: \( 9k + 26m \)
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9) \( 14n + 12p + 4n + 12p \)
- Group the \( n \)-terms: \( 14n + 4n = 18n \)
- Group the \( p \)-terms: \( 12p + 12p = 24p \)
- Combine the results: \( 18n + 24p \)
Answer: \( 18n + 24p \)
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10) \( 5a + 10b - 4a - 7b \)
- Group the \( a \)-terms: \( 5a - 4a = a \)
- Group the \( b \)-terms: \( 10b - 7b = 3b \)
- Combine the results: \( a + 3b \)
Answer: \( a + 3b \)
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Final Answers:
1. \( 13a + 7b \)
2. \( 16c + 2v \)
3. \( 21s + 10r \)
4. \( -d + 10e \)
5. \( 16f + 11g \)
6. \( 21p + 6q \)
7. \( 6b + 3c \)
8. \( 9k + 26m \)
9. \( 18n + 24p \)
10. \( a + 3b \)
\boxed{
\begin{aligned}
1. & \ 13a + 7b \\
2. & \ 16c + 2v \\
3. & \ 21s + 10r \\
4. & \ -d + 10e \\
5. & \ 16f + 11g \\
6. & \ 21p + 6q \\
7. & \ 6b + 3c \\
8. & \ 9k + 26m \\
9. & \ 18n + 24p \\
10. & \ a + 3b
\end{aligned}
}
Parent Tip: Review the logic above to help your child master the concept of collect like terms worksheet.
