Sure! Let’s solve each problem step by step. The goal is to
add or subtract polynomials by combining
like terms — terms that have the same variables raised to the same powers.
---
Problem 1:
(q³ - 2q²) - (3q² - 4q³)
→ Distribute the minus sign:
= q³ - 2q² - 3q² + 4q³
→ Combine like terms:
q³ + 4q³ =
5q³
-2q² - 3q² =
-5q²
✔ Answer: 5q³ - 5q²
---
Problem 2:
(4 + 2p³) + (5p³ + 2)
→ Remove parentheses (no distribution needed for addition):
= 4 + 2p³ + 5p³ + 2
→ Combine like terms:
2p³ + 5p³ =
7p³
4 + 2 =
6
✔ Answer: 7p³ + 6
---
Problem 3:
(3x² - x) + 5x³ + (-4x³ + x² - 8)
→ Remove parentheses:
= 3x² - x + 5x³ - 4x³ + x² - 8
→ Group like terms:
x³ terms: 5x³ - 4x³ =
x³
x² terms: 3x² + x² =
4x²
x terms:
-x
Constants:
-8
✔ Answer: x³ + 4x² - x - 8
---
Problem 4:
(8s - 1 - 7s⁴) + (7s⁴ + 1 - 2s)
→ Remove parentheses:
= 8s - 1 - 7s⁴ + 7s⁴ + 1 - 2s
→ Combine like terms:
s⁴ terms: -7s⁴ + 7s⁴ =
0
s terms: 8s - 2s =
6s
Constants: -1 + 1 =
0
✔ Answer: 6s
---
Problem 5:
(8l⁴ + 6) - (8l⁴ - 6)
→ Distribute the minus sign:
= 8l⁴ + 6 - 8l⁴ + 6
→ Combine like terms:
8l⁴ - 8l⁴ =
0
6 + 6 =
12
✔ Answer: 12
---
Problem 6:
(2p - 8p²) - (5p⁴ - 3p²)
→ Distribute the minus sign:
= 2p - 8p² - 5p⁴ + 3p²
→ Combine like terms:
p⁴ term:
-5p⁴
p² terms: -8p² + 3p² =
-5p²
p term:
2p
✔ Answer: -5p⁴ - 5p² + 2p
---
Problem 7:
(8m⁴ + m² - 4m - 8) - (1 - 4m + 3m² - m⁴)
→ Distribute the minus sign:
= 8m⁴ + m² - 4m - 8 - 1 + 4m - 3m² + m⁴
→ Combine like terms:
m⁴ terms: 8m⁴ + m⁴ =
9m⁴
m² terms: m² - 3m² =
-2m²
m terms: -4m + 4m =
0
Constants: -8 - 1 =
-9
✔ Answer: 9m⁴ - 2m² - 9
---
Problem 8:
(-9xy³ - 9x⁴y³) + (3xy³ + 7y⁴ - 8x⁴y⁴) + (3x⁴y³ + 2xy³)
→ Remove all parentheses:
= -9xy³ - 9x⁴y³ + 3xy³ + 7y⁴ - 8x⁴y⁴ + 3x⁴y³ + 2xy³
→ Group like terms:
xy³ terms: -9xy³ + 3xy³ + 2xy³ =
-4xy³
x⁴y³ terms: -9x⁴y³ + 3x⁴y³ =
-6x⁴y³
y⁴ term:
+7y⁴
x⁴y⁴ term:
-8x⁴y⁴
✔ Answer: -4xy³ - 6x⁴y³ + 7y⁴ - 8x⁴y⁴
*(Note: Terms are written in descending order of total degree or alphabetically — either is acceptable unless specified.)*
---
##
✔ Final Answers Summary:
1.
5q³ - 5q²
2.
7p³ + 6
3.
x³ + 4x² - x - 8
4.
6s
5.
12
6.
-5p⁴ - 5p² + 2p
7.
9m⁴ - 2m² - 9
8.
-4xy³ - 6x⁴y³ + 7y⁴ - 8x⁴y⁴
Let me know if you’d like these explained further or need help with graphing, factoring, or other polynomial operations! 🧮
Parent Tip: Review the logic above to help your child master the concept of algebra 1 adding and subtracting polynomials worksheet.
