SOLUTION: Adding and subtracting polynomials - Studypool - Free Printable
Educational worksheet: SOLUTION: Adding and subtracting polynomials - Studypool. Download and print for classroom or home learning activities.
PNG
793×1123
70.4 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1121814
⭐
Show Answer Key & Explanations
Step-by-step solution for: SOLUTION: Adding and subtracting polynomials - Studypool
▼
Show Answer Key & Explanations
Step-by-step solution for: SOLUTION: Adding and subtracting polynomials - Studypool
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.
We'll go through each problem one by one, simplifying them carefully.
---
Add like terms:
$-2x + 4x = 2x$,
$6 - 4 = 2$
✔ Answer: $2x + 2$
---
Distribute the minus sign:
$-4x^2 + 7x - 4x^2 - 5x$
Combine:
$-4x^2 - 4x^2 = -8x^2$,
$7x - 5x = 2x$
✔ Answer: $-8x^2 + 2x$
---
Distribute 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:
$1x + 3x = 4x$,
$9 - 7 = 2$
✔ 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: $x + 3$
---
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!
We'll go through each problem one by one, simplifying them carefully.
---
1) $(-2x + 6) + (4x - 4)$
Add 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:
$-4x^2 - 4x^2 = -8x^2$,
$7x - 5x = 2x$
✔ Answer: $-8x^2 + 2x$
---
3) $(-2x^2 + 7x) - (2x^2 + 5x)$
Distribute 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:
$1x + 3x = 4x$,
$9 - 7 = 2$
✔ 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:
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 adding and subtracting polynomials worksheet answers algebra 1.
