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.
---
Group like terms:
$$
(-2x + 4x) + (6 - 4) = 2x + 2
$$
✔ Answer: $2x + 2$
---
Distribute the minus sign:
$$
-4x^2 + 7x - 4x^2 - 5x = (-4x^2 - 4x^2) + (7x - 5x) = -8x^2 + 2x
$$
✔ Answer: $-8x^2 + 2x$
---
Distribute the minus:
$$
-2x^2 + 7x - 2x^2 - 5x = (-2x^2 - 2x^2) + (7x - 5x) = -4x^2 + 2x
$$
✔ Answer: $-4x^2 + 2x$
---
Combine like terms:
$$
(-4x^2 + 2x^2) + (3x - 2x) = -2x^2 + x
$$
✔ Answer: $-2x^2 + x$
---
Distribute the minus:
$$
5x + 9 - 4x - 7 = (5x - 4x) + (9 - 7) = x + 2
$$
✔ Answer: $x + 2$
---
Distribute:
$$
10x + 6 - 5x - 2 = (10x - 5x) + (6 - 2) = 5x + 4
$$
✔ Answer: $5x + 4$
---
Distribute:
$$
-3x^2 + 9x - 7x^2 - 7x = (-3x^2 - 7x^2) + (9x - 7x) = -10x^2 + 2x
$$
✔ Answer: $-10x^2 + 2x$
---
Add:
$$
(-10x^2 + 3x^2) + (8x - 6x) = -7x^2 + 2x
$$
✔ Answer: $-7x^2 + 2x$
---
Add:
$$
(9x + 7x) + (4 - 2) = 16x + 2
$$
✔ Answer: $16x + 2$
---
Add:
$$
(5x + 4x) + (8 - 6) = 9x + 2
$$
✔ Answer: $9x + 2$
---
Subtract:
$$
2x^2 + 7x - 2x^2 - 3x = (2x^2 - 2x^2) + (7x - 3x) = 0 + 4x = 4x
$$
✔ Answer: $4x$
---
Add:
$$
(-10x + 7x) + (4 - 3) = -3x + 1
$$
✔ Answer: $-3x + 1$
---
Add:
$$
(-4x + 2x) + (6 - 4) = -2x + 2
$$
✔ Answer: $-2x + 2$
---
Add:
$$
(8x + 3x) + (8 - 6) = 11x + 2
$$
✔ Answer: $11x + 2$
---
Distribute:
$$
10x^2 + 5x - 5x^2 - 4x = (10x^2 - 5x^2) + (5x - 4x) = 5x^2 + x
$$
✔ Answer: $5x^2 + x$
---
Distribute:
$$
-9x + 5 - 2x - 3 = (-9x - 2x) + (5 - 3) = -11x + 2
$$
✔ Answer: $-11x + 2$
---
Distribute:
$$
8x + 9 - 6x - 7 = (8x - 6x) + (9 - 7) = 2x + 2
$$
✔ Answer: $2x + 2$
---
Distribute:
$$
-8x^2 + 4x - 6x^2 - 2x = (-8x^2 - 6x^2) + (4x - 2x) = -14x^2 + 2x
$$
✔ Answer: $-14x^2 + 2x$
---
Distribute:
$$
-7x + 9 - 6x - 7 = (-7x - 6x) + (9 - 7) = -13x + 2
$$
✔ Answer: $-13x + 2$
---
Distribute:
$$
-4x + 9 - 5x - 7 = (-4x - 5x) + (9 - 7) = -9x + 2
$$
✔ Answer: $-9x + 2$
---
Add:
$$
(3x + 7x) + (4 - 3) = 10x + 1
$$
✔ Answer: $10x + 1$
---
Add:
$$
(1x + 3x) + (9 - 7) = 4x + 2
$$
✔ Answer: $4x + 2$
---
Distribute:
$$
3x + 5 - 5x - 4 = (3x - 5x) + (5 - 4) = -2x + 1
$$
✔ Answer: $-2x + 1$
---
Add:
$$
(6x + 2x) + (3 - 2) = 8x + 1
$$
✔ Answer: $8x + 1$
---
Distribute:
$$
-5x + 6 - 2x - 5 = (-5x - 2x) + (6 - 5) = -7x + 1
$$
✔ Answer: $-7x + 1$
---
Distribute:
$$
-2x + 6 - 4x - 5 = (-2x - 4x) + (6 - 5) = -6x + 1
$$
✔ Answer: $-6x + 1$
---
Add:
$$
(-9x^2 + 3x^2) + (9x - 7x) = -6x^2 + 2x
$$
✔ Answer: $-6x^2 + 2x$
---
Distribute:
$$
-10x + 7 - 7x - 5 = (-10x - 7x) + (7 - 5) = -17x + 2
$$
✔ Answer: $-17x + 2$
---
Distribute:
$$
4x^2 + 9x - 7x^2 - 7x = (4x^2 - 7x^2) + (9x - 7x) = -3x^2 + 2x
$$
✔ Answer: $-3x^2 + 2x$
---
Distribute:
$$
6x + 6 - 5x - 3 = (6x - 5x) + (6 - 3) = x + 3
$$
✔ 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 | $x + 3$ |
---
Let me know if you'd like this in a printable format or need explanations for any specific problem!
---
1) $(-2x + 6) + (4x - 4)$
Group like terms:
$$
(-2x + 4x) + (6 - 4) = 2x + 2
$$
✔ Answer: $2x + 2$
---
2) $(-4x^2 + 7x) - (4x^2 + 5x)$
Distribute the minus sign:
$$
-4x^2 + 7x - 4x^2 - 5x = (-4x^2 - 4x^2) + (7x - 5x) = -8x^2 + 2x
$$
✔ Answer: $-8x^2 + 2x$
---
3) $(-2x^2 + 7x) - (2x^2 + 5x)$
Distribute the minus:
$$
-2x^2 + 7x - 2x^2 - 5x = (-2x^2 - 2x^2) + (7x - 5x) = -4x^2 + 2x
$$
✔ Answer: $-4x^2 + 2x$
---
4) $(-4x^2 + 3x) + (2x^2 - 2x)$
Combine like terms:
$$
(-4x^2 + 2x^2) + (3x - 2x) = -2x^2 + x
$$
✔ Answer: $-2x^2 + x$
---
5) $(5x + 9) - (4x + 7)$
Distribute the minus:
$$
5x + 9 - 4x - 7 = (5x - 4x) + (9 - 7) = x + 2
$$
✔ Answer: $x + 2$
---
6) $(10x + 6) - (5x + 2)$
Distribute:
$$
10x + 6 - 5x - 2 = (10x - 5x) + (6 - 2) = 5x + 4
$$
✔ Answer: $5x + 4$
---
7) $(-3x^2 + 9x) - (7x^2 + 7x)$
Distribute:
$$
-3x^2 + 9x - 7x^2 - 7x = (-3x^2 - 7x^2) + (9x - 7x) = -10x^2 + 2x
$$
✔ Answer: $-10x^2 + 2x$
---
8) $(-10x^2 + 8x) + (3x^2 - 6x)$
Add:
$$
(-10x^2 + 3x^2) + (8x - 6x) = -7x^2 + 2x
$$
✔ Answer: $-7x^2 + 2x$
---
9) $(9x + 4) + (7x - 2)$
Add:
$$
(9x + 7x) + (4 - 2) = 16x + 2
$$
✔ Answer: $16x + 2$
---
10) $(5x + 8) + (4x - 6)$
Add:
$$
(5x + 4x) + (8 - 6) = 9x + 2
$$
✔ Answer: $9x + 2$
---
11) $(2x^2 + 7x) - (2x^2 + 3x)$
Subtract:
$$
2x^2 + 7x - 2x^2 - 3x = (2x^2 - 2x^2) + (7x - 3x) = 0 + 4x = 4x
$$
✔ Answer: $4x$
---
12) $(-10x + 4) + (7x - 3)$
Add:
$$
(-10x + 7x) + (4 - 3) = -3x + 1
$$
✔ Answer: $-3x + 1$
---
13) $(-4x + 6) + (2x - 4)$
Add:
$$
(-4x + 2x) + (6 - 4) = -2x + 2
$$
✔ Answer: $-2x + 2$
---
14) $(8x + 8) + (3x - 6)$
Add:
$$
(8x + 3x) + (8 - 6) = 11x + 2
$$
✔ Answer: $11x + 2$
---
15) $(10x^2 + 5x) - (5x^2 + 4x)$
Distribute:
$$
10x^2 + 5x - 5x^2 - 4x = (10x^2 - 5x^2) + (5x - 4x) = 5x^2 + x
$$
✔ Answer: $5x^2 + x$
---
16) $(-9x + 5) - (2x + 3)$
Distribute:
$$
-9x + 5 - 2x - 3 = (-9x - 2x) + (5 - 3) = -11x + 2
$$
✔ Answer: $-11x + 2$
---
17) $(8x + 9) - (6x + 7)$
Distribute:
$$
8x + 9 - 6x - 7 = (8x - 6x) + (9 - 7) = 2x + 2
$$
✔ Answer: $2x + 2$
---
18) $(-8x^2 + 4x) - (6x^2 + 2x)$
Distribute:
$$
-8x^2 + 4x - 6x^2 - 2x = (-8x^2 - 6x^2) + (4x - 2x) = -14x^2 + 2x
$$
✔ Answer: $-14x^2 + 2x$
---
19) $(-7x + 9) - (6x + 7)$
Distribute:
$$
-7x + 9 - 6x - 7 = (-7x - 6x) + (9 - 7) = -13x + 2
$$
✔ Answer: $-13x + 2$
---
20) $(-4x + 9) - (5x + 7)$
Distribute:
$$
-4x + 9 - 5x - 7 = (-4x - 5x) + (9 - 7) = -9x + 2
$$
✔ Answer: $-9x + 2$
---
21) $(3x + 4) + (7x - 3)$
Add:
$$
(3x + 7x) + (4 - 3) = 10x + 1
$$
✔ Answer: $10x + 1$
---
22) $(1x + 9) + (3x - 7)$
Add:
$$
(1x + 3x) + (9 - 7) = 4x + 2
$$
✔ Answer: $4x + 2$
---
23) $(3x + 5) - (5x + 4)$
Distribute:
$$
3x + 5 - 5x - 4 = (3x - 5x) + (5 - 4) = -2x + 1
$$
✔ Answer: $-2x + 1$
---
24) $(6x + 3) + (2x - 2)$
Add:
$$
(6x + 2x) + (3 - 2) = 8x + 1
$$
✔ Answer: $8x + 1$
---
25) $(-5x + 6) - (2x + 5)$
Distribute:
$$
-5x + 6 - 2x - 5 = (-5x - 2x) + (6 - 5) = -7x + 1
$$
✔ Answer: $-7x + 1$
---
26) $(-2x + 6) - (4x + 5)$
Distribute:
$$
-2x + 6 - 4x - 5 = (-2x - 4x) + (6 - 5) = -6x + 1
$$
✔ Answer: $-6x + 1$
---
27) $(-9x^2 + 9x) + (3x^2 - 7x)$
Add:
$$
(-9x^2 + 3x^2) + (9x - 7x) = -6x^2 + 2x
$$
✔ Answer: $-6x^2 + 2x$
---
28) $(-10x + 7) - (7x + 5)$
Distribute:
$$
-10x + 7 - 7x - 5 = (-10x - 7x) + (7 - 5) = -17x + 2
$$
✔ Answer: $-17x + 2$
---
29) $(4x^2 + 9x) - (7x^2 + 7x)$
Distribute:
$$
4x^2 + 9x - 7x^2 - 7x = (4x^2 - 7x^2) + (9x - 7x) = -3x^2 + 2x
$$
✔ Answer: $-3x^2 + 2x$
---
30) $(6x + 6) - (5x + 3)$
Distribute:
$$
6x + 6 - 5x - 3 = (6x - 5x) + (6 - 3) = x + 3
$$
✔ Answer: $x + 3$
---
✔ Final Answers Summary:
| 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 | $x + 3$ |
---
Let me know if you'd like this in a printable format or need explanations for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of polynomial addition and subtraction worksheet.
