Question
Polynomial Addition and Subtraction Simplify each expression. \( \begin{array}{ll}\text { 1) }\left(2 x^{4}+8\right)-\left(6 x^{4}+4\right) & \text { 2) }\left(5 v^{2}-2 v\right)+\left(3-v^{2}\right) \\ 2 \times 4+8 & \text { Period } \\ \text { 3) }\left(3 p^{4}-8+6 p^{3}\right)-\left(8 p^{4}+8-4 p^{3}\right)\end{array} \)
Ask by Hampton Cervantes. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1) -4x⁴ + 4
2) 4v² - 2v + 3
3) -5p⁴ + 10p³ - 16
Solution
We will simplify each expression by combining like terms.
1) For (2x⁴ + 8) - (6x⁴ + 4):
• Distribute the subtraction:
2x⁴ + 8 - 6x⁴ - 4
• Combine the like terms:
(2x⁴ - 6x⁴) + (8 - 4) = -4x⁴ + 4
2) For (5v² - 2v) + (3 - v²):
• Remove parentheses and group like terms:
5v² - 2v + 3 - v²
• Combine like terms:
(5v² - v²) - 2v + 3 = 4v² - 2v + 3
3) For (3p⁴ - 8 + 6p³) - (8p⁴ + 8 - 4p³):
• Distribute the subtraction:
3p⁴ - 8 + 6p³ - 8p⁴ - 8 + 4p³
• Combine like terms:
For p⁴ terms: 3p⁴ - 8p⁴ = -5p⁴
For p³ terms: 6p³ + 4p³ = 10p³
For constant terms: -8 - 8 = -16
Result: -5p⁴ + 10p³ - 16
Thus, the simplified expressions are:
1) -4x⁴ + 4
2) 4v² - 2v + 3
3) -5p⁴ + 10p³ - 16
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the polynomial expressions: 1) For \( (2x^{4}+8) - (6x^{4}+4) \): Combine like terms: \( 2x^{4} - 6x^{4} + 8 - 4 = -4x^{4} + 4 \). So, the simplified expression is \( -4x^{4} + 4 \). 2) For \( (5v^{2}-2v) + (3-v^{2}) \): Combine like terms: \( 5v^{2} - v^{2} - 2v + 3 = 4v^{2} - 2v + 3 \). The simplified expression is \( 4v^{2} - 2v + 3 \). 3) For \( (3p^{4}-8+6p^{3}) - (8p^{4}+8-4p^{3}) \): Combine like terms: \( 3p^{4} - 8p^{4} + 6p^{3} + 4p^{3} - 8 = -5p^{4} + 10p^{3} - 8 \). The simplified expression is \( -5p^{4} + 10p^{3} - 8 \).
