Adding and Subtracting Monomials worksheet - Free Printable

To solve the problem of adding and subtracting monomials, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. Here's the step-by-step solution for each problem:

---

1) \( 4c + 2c \)

- Combine the coefficients of \( c \):
\[
4c + 2c = (4 + 2)c = 6c
\]
- Answer: \( 6c \)

---

2) \( 6n + 4n + n \)

- Combine the coefficients of \( n \):
\[
6n + 4n + n = (6 + 4 + 1)n = 11n
\]
- Answer: \( 11n \)

---

3) \( 2a + 6a + 3d + 7d \)

- Combine the coefficients of \( a \):
\[
2a + 6a = (2 + 6)a = 8a
\]
- Combine the coefficients of \( d \):
\[
3d + 7d = (3 + 7)d = 10d
\]
- Answer: \( 8a + 10d \)

---

4) \( 4k + 2y + 2k \)

- Combine the coefficients of \( k \):
\[
4k + 2k = (4 + 2)k = 6k
\]
- The term \( 2y \) remains as it is because there are no other \( y \)-terms.
- Answer: \( 6k + 2y \)

---

5) \( 9k - 5k \)

- Combine the coefficients of \( k \):
\[
9k - 5k = (9 - 5)k = 4k
\]
- Answer: \( 4k \)

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6) \( 4d - 6d \)

- Combine the coefficients of \( d \):
\[
4d - 6d = (4 - 6)d = -2d
\]
- Answer: \( -2d \)

---

7) \( 5m - 2m + 3v - v \)

- Combine the coefficients of \( m \):
\[
5m - 2m = (5 - 2)m = 3m
\]
- Combine the coefficients of \( v \):
\[
3v - v = (3 - 1)v = 2v
\]
- Answer: \( 3m + 2v \)

---

8) \( 8f + 6h - 4h - 4f \)

- Combine the coefficients of \( f \):
\[
8f - 4f = (8 - 4)f = 4f
\]
- Combine the coefficients of \( h \):
\[
6h - 4h = (6 - 4)h = 2h
\]
- Answer: \( 4f + 2h \)

---

9) \( 6r - 8u - 4r + 3u \)

- Combine the coefficients of \( r \):
\[
6r - 4r = (6 - 4)r = 2r
\]
- Combine the coefficients of \( u \):
\[
-8u + 3u = (-8 + 3)u = -5u
\]
- Answer: \( 2r - 5u \)

---

10) \( 7r - 5b - 3r - 3b \)

- Combine the coefficients of \( r \):
\[
7r - 3r = (7 - 3)r = 4r
\]
- Combine the coefficients of \( b \):
\[
-5b - 3b = (-5 - 3)b = -8b
\]
- Answer: \( 4r - 8b \)

---

11) \( 6w - 2p - 3p - w \)

- Combine the coefficients of \( w \):
\[
6w - w = (6 - 1)w = 5w
\]
- Combine the coefficients of \( p \):
\[
-2p - 3p = (-2 - 3)p = -5p
\]
- Answer: \( 5w - 5p \)

---

12) \( 8f + 6h - 4h - 4f \)

- Combine the coefficients of \( f \):
\[
8f - 4f = (8 - 4)f = 4f
\]
- Combine the coefficients of \( h \):
\[
6h - 4h = (6 - 4)h = 2h
\]
- Answer: \( 4f + 2h \)

---

13) \( 3b + 3 + b + 6 \)

- Combine the coefficients of \( b \):
\[
3b + b = (3 + 1)b = 4b
\]
- Combine the constant terms:
\[
3 + 6 = 9
\]
- Answer: \( 4b + 9 \)

---

14) \( 8w + 7 - 3z - 2w \)

- Combine the coefficients of \( w \):
\[
8w - 2w = (8 - 2)w = 6w
\]
- The term \( -3z \) remains as it is because there are no other \( z \)-terms.
- Combine the constant terms:
\[
7
\]
- Answer: \( 6w - 3z + 7 \)

---

15) \( 4a - 9b + 3 - 3b - a \)

- Combine the coefficients of \( a \):
\[
4a - a = (4 - 1)a = 3a
\]
- Combine the coefficients of \( b \):
\[
-9b - 3b = (-9 - 3)b = -12b
\]
- Combine the constant terms:
\[
3
\]
- Answer: \( 3a - 12b + 3 \)

---

16) \( -3p - 4 - 7r - 4p - r - 1 \)

- Combine the coefficients of \( p \):
\[
-3p - 4p = (-3 - 4)p = -7p
\]
- Combine the coefficients of \( r \):
\[
-7r - r = (-7 - 1)r = -8r
\]
- Combine the constant terms:
\[
-4 - 1 = -5
\]
- Answer: \( -7p - 8r - 5 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ccc}
1) & 6c & \\
2) & 11n & \\
3) & 8a + 10d & \\
4) & 6k + 2y & \\
5) & 4k & \\
6) & -2d & \\
7) & 3m + 2v & \\
8) & 4f + 2h & \\
9) & 2r - 5u & \\
10) & 4r - 8b & \\
11) & 5w - 5p & \\
12) & 4f + 2h & \\
13) & 4b + 9 & \\
14) & 6w - 3z + 7 & \\
15) & 3a - 12b + 3 & \\
16) & -7p - 8r - 5 &
\end{array}
}
\]