To solve the problem of combining like terms, we need to group and simplify terms that have the same variable. Let's go through each expression step by step.
Expression 1: \( 3x + 5x + 2y \)
- Combine the \( x \)-terms: \( 3x + 5x = 8x \)
- The \( y \)-term remains as it is: \( 2y \)
- Simplified expression: \( 8x + 2y \)
Expression 2: \( 2a - 4b + 3a + b \)
- Combine the \( a \)-terms: \( 2a + 3a = 5a \)
- Combine the \( b \)-terms: \( -4b + b = -3b \)
- Simplified expression: \( 5a - 3b \)
Expression 3: \( 6m + 2n - 3m + 5n \)
- Combine the \( m \)-terms: \( 6m - 3m = 3m \)
- Combine the \( n \)-terms: \( 2n + 5n = 7n \)
- Simplified expression: \( 3m + 7n \)
Expression 4: \( 4p - 7q - 2p + 9q \)
- Combine the \( p \)-terms: \( 4p - 2p = 2p \)
- Combine the \( q \)-terms: \( -7q + 9q = 2q \)
- Simplified expression: \( 2p + 2q \)
Expression 5: \( 8x + 3y - 2x - 6y \)
- Combine the \( x \)-terms: \( 8x - 2x = 6x \)
- Combine the \( y \)-terms: \( 3y - 6y = -3y \)
- Simplified expression: \( 6x - 3y \)
Expression 6: \( 5a + 2b - 3a + 4b \)
- Combine the \( a \)-terms: \( 5a - 3a = 2a \)
- Combine the \( b \)-terms: \( 2b + 4b = 6b \)
- Simplified expression: \( 2a + 6b \)
Expression 7: \( 2m - 9n + 7m + 5n \)
- Combine the \( m \)-terms: \( 2m + 7m = 9m \)
- Combine the \( n \)-terms: \( -9n + 5n = -4n \)
- Simplified expression: \( 9m - 4n \)
Expression 8: \( 6x + 3y - 4x - 2y \)
- Combine the \( x \)-terms: \( 6x - 4x = 2x \)
- Combine the \( y \)-terms: \( 3y - 2y = y \)
- Simplified expression: \( 2x + y \)
Expression 9: \( 4a - 5b + 2c - 3a + 4b - c \)
- Combine the \( a \)-terms: \( 4a - 3a = a \)
- Combine the \( b \)-terms: \( -5b + 4b = -b \)
- Combine the \( c \)-terms: \( 2c - c = c \)
- Simplified expression: \( a - b + c \)
Final Answers:
\[
\boxed{
\begin{array}{ll}
3x + 5x + 2y & 8x + 2y \\
2a - 4b + 3a + b & 5a - 3b \\
6m + 2n - 3m + 5n & 3m + 7n \\
4p - 7q - 2p + 9q & 2p + 2q \\
8x + 3y - 2x - 6y & 6x - 3y \\
5a + 2b - 3a + 4b & 2a + 6b \\
2m - 9n + 7m + 5n & 9m - 4n \\
6x + 3y - 4x - 2y & 2x + y \\
4a - 5b + 2c - 3a + 4b - c & a - b + c \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of worksheet combining like terms.
