To simplify the given expressions, we need to collect and combine like terms. Like terms are terms that have the same variable(s) raised to the same power. Here's the step-by-step solution for each expression:
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a) \( 2x + 6y + 7x \)
- Combine the \( x \)-terms: \( 2x + 7x = 9x \)
- The \( y \)-term remains as it is: \( 6y \)
Simplified Expression:
\[ 9x + 6y \]
---
b) \( 3a + 8b + 5a \)
- Combine the \( a \)-terms: \( 3a + 5a = 8a \)
- The \( b \)-term remains as it is: \( 8b \)
Simplified Expression:
\[ 8a + 8b \]
---
c) \( 6u + 3v - 2u \)
- Combine the \( u \)-terms: \( 6u - 2u = 4u \)
- The \( v \)-term remains as it is: \( 3v \)
Simplified Expression:
\[ 4u + 3v \]
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d) \( 9p + 8q - p \)
- Combine the \( p \)-terms: \( 9p - p = 8p \)
- The \( q \)-term remains as it is: \( 8q \)
Simplified Expression:
\[ 8p + 8q \]
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e) \( 2m + 5n + 4m + 3n \)
- Combine the \( m \)-terms: \( 2m + 4m = 6m \)
- Combine the \( n \)-terms: \( 5n + 3n = 8n \)
Simplified Expression:
\[ 6m + 8n \]
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f) \( 6u + 9v + u + 3v \)
- Combine the \( u \)-terms: \( 6u + u = 7u \)
- Combine the \( v \)-terms: \( 9v + 3v = 12v \)
Simplified Expression:
\[ 7u + 12v \]
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g) \( 8b + 7c + 3b - 2c \)
- Combine the \( b \)-terms: \( 8b + 3b = 11b \)
- Combine the \( c \)-terms: \( 7c - 2c = 5c \)
Simplified Expression:
\[ 11b + 5c \]
---
h) \( a + 2b + a - b \)
- Combine the \( a \)-terms: \( a + a = 2a \)
- Combine the \( b \)-terms: \( 2b - b = b \)
Simplified Expression:
\[ 2a + b \]
---
i) \( 5a + 2b - 5a + 6b \)
- Combine the \( a \)-terms: \( 5a - 5a = 0 \)
- Combine the \( b \)-terms: \( 2b + 6b = 8b \)
Simplified Expression:
\[ 8b \]
---
j) \( 9p + 3q - 2p - 3q \)
- Combine the \( p \)-terms: \( 9p - 2p = 7p \)
- Combine the \( q \)-terms: \( 3q - 3q = 0 \)
Simplified Expression:
\[ 7p \]
---
Final Answers:
\[
\boxed{
\begin{aligned}
&\text{a) } 9x + 6y \\
&\text{b) } 8a + 8b \\
&\text{c) } 4u + 3v \\
&\text{d) } 8p + 8q \\
&\text{e) } 6m + 8n \\
&\text{f) } 7u + 12v \\
&\text{g) } 11b + 5c \\
&\text{h) } 2a + b \\
&\text{i) } 8b \\
&\text{j) } 7p
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of addition expressions worksheet.
