Free custom combining like terms worksheet templates - Free Printable

Problem: Simplify the algebraic expressions by combining like terms.

#### Easy Level

1. Expression: \( 3x + 2y + 5x \)
- Solution:
- Combine the \( x \)-terms: \( 3x + 5x = 8x \)
- The \( y \)-term remains as it is: \( 2y \)
- Simplified Expression: \( 8x + 2y \)

2. Expression: \( 7p - 3q - 2p + 5q \)
- Solution:
- Combine the \( p \)-terms: \( 7p - 2p = 5p \)
- Combine the \( q \)-terms: \( -3q + 5q = 2q \)
- Simplified Expression: \( 5p + 2q \)

3. Expression: \( 4a - 2b + 2a + 3b \)
- Solution:
- Combine the \( a \)-terms: \( 4a + 2a = 6a \)
- Combine the \( b \)-terms: \( -2b + 3b = b \)
- Simplified Expression: \( 6a + b \)

4. Expression: \( 6x + 2y + 3x - 4y \)
- Solution:
- Combine the \( x \)-terms: \( 6x + 3x = 9x \)
- Combine the \( y \)-terms: \( 2y - 4y = -2y \)
- Simplified Expression: \( 9x - 2y \)

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#### Medium Level

1. Expression: \( 3a + 2b - 4a + 5b \)
- Solution:
- Combine the \( a \)-terms: \( 3a - 4a = -a \)
- Combine the \( b \)-terms: \( 2b + 5b = 7b \)
- Simplified Expression: \( -a + 7b \)

2. Expression: \( 4x + 2y + 3x - y \)
- Solution:
- Combine the \( x \)-terms: \( 4x + 3x = 7x \)
- Combine the \( y \)-terms: \( 2y - y = y \)
- Simplified Expression: \( 7x + y \)

3. Expression: \( 5m - 2n + 3m + 2n \)
- Solution:
- Combine the \( m \)-terms: \( 5m + 3m = 8m \)
- Combine the \( n \)-terms: \( -2n + 2n = 0 \)
- Simplified Expression: \( 8m \)

4. Expression: \( 8c - 2d + 4c - 3d \)
- Solution:
- Combine the \( c \)-terms: \( 8c + 4c = 12c \)
- Combine the \( d \)-terms: \( -2d - 3d = -5d \)
- Simplified Expression: \( 12c - 5d \)

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#### Hard Level

1. Expression: \( 2x + 3y - 4x + 5y - 3z \)
- Solution:
- Combine the \( x \)-terms: \( 2x - 4x = -2x \)
- Combine the \( y \)-terms: \( 3y + 5y = 8y \)
- The \( z \)-term remains as it is: \( -3z \)
- Simplified Expression: \( -2x + 8y - 3z \)

2. Expression: \( 5a^2 + 2b - 3a^2 - 6b \)
- Solution:
- Combine the \( a^2 \)-terms: \( 5a^2 - 3a^2 = 2a^2 \)
- Combine the \( b \)-terms: \( 2b - 6b = -4b \)
- Simplified Expression: \( 2a^2 - 4b \)

3. Expression: \( 4p^3 + 3q - 2p^3 + 5q \)
- Solution:
- Combine the \( p^3 \)-terms: \( 4p^3 - 2p^3 = 2p^3 \)
- Combine the \( q \)-terms: \( 3q + 5q = 8q \)
- Simplified Expression: \( 2p^3 + 8q \)

4. Expression: \( 6ab^2 - 3bc^2 + 5ab^2 + 4bc^2 \)
- Solution:
- Combine the \( ab^2 \)-terms: \( 6ab^2 + 5ab^2 = 11ab^2 \)
- Combine the \( bc^2 \)-terms: \( -3bc^2 + 4bc^2 = bc^2 \)
- Simplified Expression: \( 11ab^2 + bc^2 \)

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Final Answers:

- Easy:
1. \( 8x + 2y \)
2. \( 5p + 2q \)
3. \( 6a + b \)
4. \( 9x - 2y \)

- Medium:
1. \( -a + 7b \)
2. \( 7x + y \)
3. \( 8m \)
4. \( 12c - 5d \)

- Hard:
1. \( -2x + 8y - 3z \)
2. \( 2a^2 - 4b \)
3. \( 2p^3 + 8q \)
4. \( 11ab^2 + bc^2 \)

\boxed{
\begin{aligned}
&\text{Easy: } 8x + 2y, 5p + 2q, 6a + b, 9x - 2y \\
&\text{Medium: } -a + 7b, 7x + y, 8m, 12c - 5d \\
&\text{Hard: } -2x + 8y - 3z, 2a^2 - 4b, 2p^3 + 8q, 11ab^2 + bc^2
\end{aligned}
}