Answer/Step-by-step explanation:
7. (3x⁴ + 5x² - 1) + (2x³ + x)
Distribute +1 to each term in the parentheses by your right.
3x⁴ + 5x² - 1 + 2x³ + x
Rewrite in standard form
3x⁴ + 2x¾ + 5x² + x - 1
8. (4x² + 7x - 4) + (x² - 7x + 14)
Distribute +1 to each term in the parentheses by your right.
4x² + 7x - 4 + x² - 7x + 14
Collect like terms and add together
4x² + x² + 7x - 7x - 4 + 14
5x² + 10
9. (2x³ + 6x² - 5x) + (x⁵ + 3x² + 8x + 4)
2x³ + 6x² - 5x + x⁵ + 3x² + 8x + 4
Collect like terms and add together
2x³ + 6x² + 3x² - 5x + 8x + x⁵ + 4
2x³ + 9x² + 3x + x⁵ + 4
Rewrite in standard form
x⁵ + 2x³ + 9x² + 3x + 4
10. (-6x⁵ - 2x + 13) + (4x⁵ + 3x² + x - 9)
-6x⁵ - 2x + 13 + 4x⁵ + 3x² + x - 9
Collect like terms
-6x⁵ + 4x⁵ - 2x + x + 13 - 9 + 3x²
Add like terms
-2x⁵ - x + 4 + 3x²
Rewrite in standard form
-2x⁵ + 3x² - x + 4
11. (5x² + 7x + 2) - (3x² + 6x + 2)
Distribute -1 to each term in the parentheses by your right.
5x² + 7x + 2 - 3x² - 6x - 2
Collect like terms
5x² - 3x² + 7x - 6x + 2 - 2
2x² + x
12. (10x⁴ + 2x² + 1) - (3x⁴ + 3x + 11)
Distribute -1 to each term in the parentheses by your right.
10x⁴ + 2x² + 1 - 3x⁴ - 3x - 11
Collect like terms
10x⁴ - 3x⁴ + 2x² + 1 - 11 - 3x
7x⁴ + 2x² - 10 - 3x
Rewrite in standard form
7x⁴ + 2x² - 3x - 10
13. (7x³ - 3x + 7) - (4x² - 3x - 11)
Distribute -1 to each term in the parentheses by your right.
7x³ - 3x + 7 - 4x² + 3x + 11
Collect like terms
7x³ - 3x + 3x + 7 + 11 - 4x²
7x³ + 18 - 4x²
Rewrite in standard form
7x³ - 4x² + 18
14. (x⁴ - 1) - (x⁴ + 1)
Distribute -1 to each term in the parentheses by your right.
x⁴ - 1 - x⁴ - 1
Collect like terms
x⁴ - x⁴ - 1 - 1
-2
