Adding and Subtracting Polynomials worksheets - Free Printable
Educational worksheet: Adding and Subtracting Polynomials worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Adding and Subtracting Polynomials worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Adding and Subtracting Polynomials worksheets
Let's solve each of these polynomial addition and subtraction problems step by step. The key idea is to combine like terms — that is, terms with the same variable and exponent.
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Group like terms:
- $-2x + 4x = 2x$
- $6 - 4 = 2$
✔ Answer: $2x + 2$
---
Distribute the minus sign:
- $-4x^2 + 7x - 4x^2 - 5x$
Combine like terms:
- $-4x^2 - 4x^2 = -8x^2$
- $7x - 5x = 2x$
✔ Answer: $-8x^2 + 2x$
---
Distribute the minus:
- $-2x^2 + 7x - 2x^2 - 5x$
Combine:
- $-2x^2 - 2x^2 = -4x^2$
- $7x - 5x = 2x$
✔ Answer: $-4x^2 + 2x$
---
Add like terms:
- $-4x^2 + 2x^2 = -2x^2$
- $3x - 2x = x$
✔ Answer: $-2x^2 + x$
---
Distribute minus:
- $5x + 9 - 4x - 7$
Combine:
- $5x - 4x = x$
- $9 - 7 = 2$
✔ Answer: $x + 2$
---
Distribute minus:
- $10x + 6 - 5x - 2$
Combine:
- $10x - 5x = 5x$
- $6 - 2 = 4$
✔ Answer: $5x + 4$
---
Distribute minus:
- $-3x^2 + 9x - 7x^2 - 7x$
Combine:
- $-3x^2 - 7x^2 = -10x^2$
- $9x - 7x = 2x$
✔ Answer: $-10x^2 + 2x$
---
Add like terms:
- $-10x^2 + 3x^2 = -7x^2$
- $8x - 6x = 2x$
✔ Answer: $-7x^2 + 2x$
---
Add:
- $9x + 7x = 16x$
- $4 - 2 = 2$
✔ Answer: $16x + 2$
---
Add:
- $5x + 4x = 9x$
- $8 - 6 = 2$
✔ Answer: $9x + 2$
---
Distribute minus:
- $2x^2 + 7x - 2x^2 - 3x$
Combine:
- $2x^2 - 2x^2 = 0$
- $7x - 3x = 4x$
✔ Answer: $4x$
---
Add:
- $-10x + 7x = -3x$
- $4 - 3 = 1$
✔ Answer: $-3x + 1$
---
Add:
- $-4x + 2x = -2x$
- $6 - 4 = 2$
✔ Answer: $-2x + 2$
---
Add:
- $8x + 3x = 11x$
- $8 - 6 = 2$
✔ Answer: $11x + 2$
---
Distribute minus:
- $10x^2 + 5x - 5x^2 - 4x$
Combine:
- $10x^2 - 5x^2 = 5x^2$
- $5x - 4x = x$
✔ Answer: $5x^2 + x$
---
Distribute minus:
- $-9x + 5 - 2x - 3$
Combine:
- $-9x - 2x = -11x$
- $5 - 3 = 2$
✔ Answer: $-11x + 2$
---
Distribute minus:
- $8x + 9 - 6x - 7$
Combine:
- $8x - 6x = 2x$
- $9 - 7 = 2$
✔ Answer: $2x + 2$
---
Distribute minus:
- $-8x^2 + 4x - 6x^2 - 2x$
Combine:
- $-8x^2 - 6x^2 = -14x^2$
- $4x - 2x = 2x$
✔ Answer: $-14x^2 + 2x$
---
Distribute minus:
- $-7x + 9 - 6x - 7$
Combine:
- $-7x - 6x = -13x$
- $9 - 7 = 2$
✔ Answer: $-13x + 2$
---
Distribute minus:
- $-4x + 9 - 5x - 7$
Combine:
- $-4x - 5x = -9x$
- $9 - 7 = 2$
✔ Answer: $-9x + 2$
---
Add:
- $3x + 7x = 10x$
- $4 - 3 = 1$
✔ Answer: $10x + 1$
---
Add:
- $x + 3x = 4x$
- $9 - 7 = 2$
✔ Answer: $4x + 2$
---
Distribute minus:
- $3x + 5 - 5x - 4$
Combine:
- $3x - 5x = -2x$
- $5 - 4 = 1$
✔ Answer: $-2x + 1$
---
Add:
- $6x + 2x = 8x$
- $3 - 2 = 1$
✔ Answer: $8x + 1$
---
Distribute minus:
- $-5x + 6 - 2x - 5$
Combine:
- $-5x - 2x = -7x$
- $6 - 5 = 1$
✔ Answer: $-7x + 1$
---
Distribute minus:
- $-2x + 6 - 4x - 5$
Combine:
- $-2x - 4x = -6x$
- $6 - 5 = 1$
✔ Answer: $-6x + 1$
---
Add:
- $-9x^2 + 3x^2 = -6x^2$
- $9x - 7x = 2x$
✔ Answer: $-6x^2 + 2x$
---
Distribute minus:
- $-10x + 7 - 7x - 5$
Combine:
- $-10x - 7x = -17x$
- $7 - 5 = 2$
✔ Answer: $-17x + 2$
---
Distribute minus:
- $4x^2 + 9x - 7x^2 - 7x$
Combine:
- $4x^2 - 7x^2 = -3x^2$
- $9x - 7x = 2x$
✔ Answer: $-3x^2 + 2x$
---
Distribute minus:
- $6x + 6 - 5x - 3$
Combine:
- $6x - 5x = x$
- $6 - 3 = 3$
✔ Answer: $x + 3$
---
| Problem | Answer |
|--------|--------|
| 1 | $2x + 2$ |
| 2 | $-8x^2 + 2x$ |
| 3 | $-4x^2 + 2x$ |
| 4 | $-2x^2 + x$ |
| 5 | $x + 2$ |
| 6 | $5x + 4$ |
| 7 | $-10x^2 + 2x$ |
| 8 | $-7x^2 + 2x$ |
| 9 | $16x + 2$ |
| 10 | $9x + 2$ |
| 11 | $4x$ |
| 12 | $-3x + 1$ |
| 13 | $-2x + 2$ |
| 14 | $11x + 2$ |
| 15 | $5x^2 + x$ |
| 16 | $-11x + 2$ |
| 17 | $2x + 2$ |
| 18 | $-14x^2 + 2x$ |
| 19 | $-13x + 2$ |
| 20 | $-9x + 2$ |
| 21 | $10x + 1$ |
| 22 | $4x + 2$ |
| 23 | $-2x + 1$ |
| 24 | $8x + 1$ |
| 25 | $-7x + 1$ |
| 26 | $-6x + 1$ |
| 27 | $-6x^2 + 2x$ |
| 28 | $-17x + 2$ |
| 29 | $-3x^2 + 2x$ |
| 30 | $x + 3$ |
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Let me know if you'd like this as a downloadable PDF or need help checking your work!
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1) $(-2x + 6) + (4x - 4)$
Group like terms:
- $-2x + 4x = 2x$
- $6 - 4 = 2$
✔ Answer: $2x + 2$
---
2) $(-4x^2 + 7x) - (4x^2 + 5x)$
Distribute the minus sign:
- $-4x^2 + 7x - 4x^2 - 5x$
Combine like terms:
- $-4x^2 - 4x^2 = -8x^2$
- $7x - 5x = 2x$
✔ Answer: $-8x^2 + 2x$
---
3) $(-2x^2 + 7x) - (2x^2 + 5x)$
Distribute the minus:
- $-2x^2 + 7x - 2x^2 - 5x$
Combine:
- $-2x^2 - 2x^2 = -4x^2$
- $7x - 5x = 2x$
✔ Answer: $-4x^2 + 2x$
---
4) $(-4x^2 + 3x) + (2x^2 - 2x)$
Add like terms:
- $-4x^2 + 2x^2 = -2x^2$
- $3x - 2x = x$
✔ Answer: $-2x^2 + x$
---
5) $(5x + 9) - (4x + 7)$
Distribute minus:
- $5x + 9 - 4x - 7$
Combine:
- $5x - 4x = x$
- $9 - 7 = 2$
✔ Answer: $x + 2$
---
6) $(10x + 6) - (5x + 2)$
Distribute minus:
- $10x + 6 - 5x - 2$
Combine:
- $10x - 5x = 5x$
- $6 - 2 = 4$
✔ Answer: $5x + 4$
---
7) $(-3x^2 + 9x) - (7x^2 + 7x)$
Distribute minus:
- $-3x^2 + 9x - 7x^2 - 7x$
Combine:
- $-3x^2 - 7x^2 = -10x^2$
- $9x - 7x = 2x$
✔ Answer: $-10x^2 + 2x$
---
8) $(-10x^2 + 8x) + (3x^2 - 6x)$
Add like terms:
- $-10x^2 + 3x^2 = -7x^2$
- $8x - 6x = 2x$
✔ Answer: $-7x^2 + 2x$
---
9) $(9x + 4) + (7x - 2)$
Add:
- $9x + 7x = 16x$
- $4 - 2 = 2$
✔ Answer: $16x + 2$
---
10) $(5x + 8) + (4x - 6)$
Add:
- $5x + 4x = 9x$
- $8 - 6 = 2$
✔ Answer: $9x + 2$
---
11) $(2x^2 + 7x) - (2x^2 + 3x)$
Distribute minus:
- $2x^2 + 7x - 2x^2 - 3x$
Combine:
- $2x^2 - 2x^2 = 0$
- $7x - 3x = 4x$
✔ Answer: $4x$
---
12) $(-10x + 4) + (7x - 3)$
Add:
- $-10x + 7x = -3x$
- $4 - 3 = 1$
✔ Answer: $-3x + 1$
---
13) $(-4x + 6) + (2x - 4)$
Add:
- $-4x + 2x = -2x$
- $6 - 4 = 2$
✔ Answer: $-2x + 2$
---
14) $(8x + 8) + (3x - 6)$
Add:
- $8x + 3x = 11x$
- $8 - 6 = 2$
✔ Answer: $11x + 2$
---
15) $(10x^2 + 5x) - (5x^2 + 4x)$
Distribute minus:
- $10x^2 + 5x - 5x^2 - 4x$
Combine:
- $10x^2 - 5x^2 = 5x^2$
- $5x - 4x = x$
✔ Answer: $5x^2 + x$
---
16) $(-9x + 5) - (2x + 3)$
Distribute minus:
- $-9x + 5 - 2x - 3$
Combine:
- $-9x - 2x = -11x$
- $5 - 3 = 2$
✔ Answer: $-11x + 2$
---
17) $(8x + 9) - (6x + 7)$
Distribute minus:
- $8x + 9 - 6x - 7$
Combine:
- $8x - 6x = 2x$
- $9 - 7 = 2$
✔ Answer: $2x + 2$
---
18) $(-8x^2 + 4x) - (6x^2 + 2x)$
Distribute minus:
- $-8x^2 + 4x - 6x^2 - 2x$
Combine:
- $-8x^2 - 6x^2 = -14x^2$
- $4x - 2x = 2x$
✔ Answer: $-14x^2 + 2x$
---
19) $(-7x + 9) - (6x + 7)$
Distribute minus:
- $-7x + 9 - 6x - 7$
Combine:
- $-7x - 6x = -13x$
- $9 - 7 = 2$
✔ Answer: $-13x + 2$
---
20) $(-4x + 9) - (5x + 7)$
Distribute minus:
- $-4x + 9 - 5x - 7$
Combine:
- $-4x - 5x = -9x$
- $9 - 7 = 2$
✔ Answer: $-9x + 2$
---
21) $(3x + 4) + (7x - 3)$
Add:
- $3x + 7x = 10x$
- $4 - 3 = 1$
✔ Answer: $10x + 1$
---
22) $(1x + 9) + (3x - 7)$
Add:
- $x + 3x = 4x$
- $9 - 7 = 2$
✔ Answer: $4x + 2$
---
23) $(3x + 5) - (5x + 4)$
Distribute minus:
- $3x + 5 - 5x - 4$
Combine:
- $3x - 5x = -2x$
- $5 - 4 = 1$
✔ Answer: $-2x + 1$
---
24) $(6x + 3) + (2x - 2)$
Add:
- $6x + 2x = 8x$
- $3 - 2 = 1$
✔ Answer: $8x + 1$
---
25) $(-5x + 6) - (2x + 5)$
Distribute minus:
- $-5x + 6 - 2x - 5$
Combine:
- $-5x - 2x = -7x$
- $6 - 5 = 1$
✔ Answer: $-7x + 1$
---
26) $(-2x + 6) - (4x + 5)$
Distribute minus:
- $-2x + 6 - 4x - 5$
Combine:
- $-2x - 4x = -6x$
- $6 - 5 = 1$
✔ Answer: $-6x + 1$
---
27) $(-9x^2 + 9x) + (3x^2 - 7x)$
Add:
- $-9x^2 + 3x^2 = -6x^2$
- $9x - 7x = 2x$
✔ Answer: $-6x^2 + 2x$
---
28) $(-10x + 7) - (7x + 5)$
Distribute minus:
- $-10x + 7 - 7x - 5$
Combine:
- $-10x - 7x = -17x$
- $7 - 5 = 2$
✔ Answer: $-17x + 2$
---
29) $(4x^2 + 9x) - (7x^2 + 7x)$
Distribute minus:
- $4x^2 + 9x - 7x^2 - 7x$
Combine:
- $4x^2 - 7x^2 = -3x^2$
- $9x - 7x = 2x$
✔ Answer: $-3x^2 + 2x$
---
30) $(6x + 6) - (5x + 3)$
Distribute minus:
- $6x + 6 - 5x - 3$
Combine:
- $6x - 5x = x$
- $6 - 3 = 3$
✔ Answer: $x + 3$
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | $2x + 2$ |
| 2 | $-8x^2 + 2x$ |
| 3 | $-4x^2 + 2x$ |
| 4 | $-2x^2 + x$ |
| 5 | $x + 2$ |
| 6 | $5x + 4$ |
| 7 | $-10x^2 + 2x$ |
| 8 | $-7x^2 + 2x$ |
| 9 | $16x + 2$ |
| 10 | $9x + 2$ |
| 11 | $4x$ |
| 12 | $-3x + 1$ |
| 13 | $-2x + 2$ |
| 14 | $11x + 2$ |
| 15 | $5x^2 + x$ |
| 16 | $-11x + 2$ |
| 17 | $2x + 2$ |
| 18 | $-14x^2 + 2x$ |
| 19 | $-13x + 2$ |
| 20 | $-9x + 2$ |
| 21 | $10x + 1$ |
| 22 | $4x + 2$ |
| 23 | $-2x + 1$ |
| 24 | $8x + 1$ |
| 25 | $-7x + 1$ |
| 26 | $-6x + 1$ |
| 27 | $-6x^2 + 2x$ |
| 28 | $-17x + 2$ |
| 29 | $-3x^2 + 2x$ |
| 30 | $x + 3$ |
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Let me know if you'd like this as a downloadable PDF or need help checking your work!
Parent Tip: Review the logic above to help your child master the concept of adding polynomials worksheet answers.
