Add & Subtract Polynomial Worksheets (printable, online, answers ... - Free Printable

To simplify each polynomial expression, we need to combine like terms. Let's go through each problem step by step.

---

Problem 1:

\[
(7c - 5c^4) + (9c - 2c^4 + 3)
\]

#### Step 1: Write out the expression.
\[
7c - 5c^4 + 9c - 2c^4 + 3
\]

#### Step 2: Group like terms.
- Terms involving \( c \): \( 7c \) and \( 9c \)
- Terms involving \( c^4 \): \( -5c^4 \) and \( -2c^4 \)
- Constant term: \( 3 \)

\[
(7c + 9c) + (-5c^4 - 2c^4) + 3
\]

#### Step 3: Simplify each group.
- \( 7c + 9c = 16c \)
- \( -5c^4 - 2c^4 = -7c^4 \)
- The constant term remains \( 3 \)

\[
16c - 7c^4 + 3
\]

#### Final Answer:
\[
\boxed{-7c^4 + 16c + 3}
\]

---

Problem 2:

\[
(5 - 7g^2) + (6g^4 + 2 + 3g^2)
\]

#### Step 1: Write out the expression.
\[
5 - 7g^2 + 6g^4 + 2 + 3g^2
\]

#### Step 2: Group like terms.
- Terms involving \( g^4 \): \( 6g^4 \)
- Terms involving \( g^2 \): \( -7g^2 \) and \( 3g^2 \)
- Constant terms: \( 5 \) and \( 2 \)

\[
6g^4 + (-7g^2 + 3g^2) + (5 + 2)
\]

#### Step 3: Simplify each group.
- \( -7g^2 + 3g^2 = -4g^2 \)
- \( 5 + 2 = 7 \)

\[
6g^4 - 4g^2 + 7
\]

#### Final Answer:
\[
\boxed{6g^4 - 4g^2 + 7}
\]

---

Problem 3:

\[
(7 + 2s^4) + (4s^5 - 9 - 3s^4)
\]

#### Step 1: Write out the expression.
\[
7 + 2s^4 + 4s^5 - 9 - 3s^4
\]

#### Step 2: Group like terms.
- Terms involving \( s^5 \): \( 4s^5 \)
- Terms involving \( s^4 \): \( 2s^4 \) and \( -3s^4 \)
- Constant terms: \( 7 \) and \( -9 \)

\[
4s^5 + (2s^4 - 3s^4) + (7 - 9)
\]

#### Step 3: Simplify each group.
- \( 2s^4 - 3s^4 = -s^4 \)
- \( 7 - 9 = -2 \)

\[
4s^5 - s^4 - 2
\]

#### Final Answer:
\[
\boxed{4s^5 - s^4 - 2}
\]

---

Problem 4:

\[
(4h^5 + 2) + (9h^5 - 7 - 5h^2)
\]

#### Step 1: Write out the expression.
\[
4h^5 + 2 + 9h^5 - 7 - 5h^2
\]

#### Step 2: Group like terms.
- Terms involving \( h^5 \): \( 4h^5 \) and \( 9h^5 \)
- Terms involving \( h^2 \): \( -5h^2 \)
- Constant terms: \( 2 \) and \( -7 \)

\[
(4h^5 + 9h^5) - 5h^2 + (2 - 7)
\]

#### Step 3: Simplify each group.
- \( 4h^5 + 9h^5 = 13h^5 \)
- \( 2 - 7 = -5 \)

\[
13h^5 - 5h^2 - 5
\]

#### Final Answer:
\[
\boxed{13h^5 - 5h^2 - 5}
\]

---

Problem 5:

\[
(2x^4 - 4x^3) + (6x^3 + 9x - 5x^4)
\]

#### Step 1: Write out the expression.
\[
2x^4 - 4x^3 + 6x^3 + 9x - 5x^4
\]

#### Step 2: Group like terms.
- Terms involving \( x^4 \): \( 2x^4 \) and \( -5x^4 \)
- Terms involving \( x^3 \): \( -4x^3 \) and \( 6x^3 \)
- Terms involving \( x \): \( 9x \)

\[
(2x^4 - 5x^4) + (-4x^3 + 6x^3) + 9x
\]

#### Step 3: Simplify each group.
- \( 2x^4 - 5x^4 = -3x^4 \)
- \( -4x^3 + 6x^3 = 2x^3 \)
- The \( x \)-term remains \( 9x \)

\[
-3x^4 + 2x^3 + 9x
\]

#### Final Answer:
\[
\boxed{-3x^4 + 2x^3 + 9x}
\]

---

Problem 6:

\[
(2b + 9 - 7b^3) + (8b^3 - 6 - 4b^5)
\]

#### Step 1: Write out the expression.
\[
2b + 9 - 7b^3 + 8b^3 - 6 - 4b^5
\]

#### Step 2: Group like terms.
- Terms involving \( b^5 \): \( -4b^5 \)
- Terms involving \( b^3 \): \( -7b^3 \) and \( 8b^3 \)
- Terms involving \( b \): \( 2b \)
- Constant terms: \( 9 \) and \( -6 \)

\[
-4b^5 + (-7b^3 + 8b^3) + 2b + (9 - 6)
\]

#### Step 3: Simplify each group.
- \( -7b^3 + 8b^3 = b^3 \)
- \( 9 - 6 = 3 \)

\[
-4b^5 + b^3 + 2b + 3
\]

#### Final Answer:
\[
\boxed{-4b^5 + b^3 + 2b + 3}
\]

---

Problem 7:

\[
(2 - 6p^2 - 5p^4) + (9p - 8p^4 + 4)
\]

#### Step 1: Write out the expression.
\[
2 - 6p^2 - 5p^4 + 9p - 8p^4 + 4
\]

#### Step 2: Group like terms.
- Terms involving \( p^4 \): \( -5p^4 \) and \( -8p^4 \)
- Terms involving \( p^2 \): \( -6p^2 \)
- Terms involving \( p \): \( 9p \)
- Constant terms: \( 2 \) and \( 4 \)

\[
(-5p^4 - 8p^4) - 6p^2 + 9p + (2 + 4)
\]

#### Step 3: Simplify each group.
- \( -5p^4 - 8p^4 = -13p^4 \)
- \( 2 + 4 = 6 \)

\[
-13p^4 - 6p^2 + 9p + 6
\]

#### Final Answer:
\[
\boxed{-13p^4 - 6p^2 + 9p + 6}
\]

---

Problem 8:

\[
(6z^3 - 9) + (5z^3 - 8 + z^4)
\]

#### Step 1: Write out the expression.
\[
6z^3 - 9 + 5z^3 - 8 + z^4
\]

#### Step 2: Group like terms.
- Terms involving \( z^4 \): \( z^4 \)
- Terms involving \( z^3 \): \( 6z^3 \) and \( 5z^3 \)
- Constant terms: \( -9 \) and \( -8 \)

\[
z^4 + (6z^3 + 5z^3) + (-9 - 8)
\]

#### Step 3: Simplify each group.
- \( 6z^3 + 5z^3 = 11z^3 \)
- \( -9 - 8 = -17 \)

\[
z^4 + 11z^3 - 17
\]

#### Final Answer:
\[
\boxed{z^4 + 11z^3 - 17}
\]

---

Final Answers:

1. \(\boxed{-7c^4 + 16c + 3}\)
2. \(\boxed{6g^4 - 4g^2 + 7}\)
3. \(\boxed{4s^5 - s^4 - 2}\)
4. \(\boxed{13h^5 - 5h^2 - 5}\)
5. \(\boxed{-3x^4 + 2x^3 + 9x}\)
6. \(\boxed{-4b^5 + b^3 + 2b + 3}\)
7. \(\boxed{-13p^4 - 6p^2 + 9p + 6}\)
8. \(\boxed{z^4 + 11z^3 - 17}\)