Question

1. (13m² + 6m² - 2m) - (-10m² - 13m² + 9m)

(15e⁵ + 5e³ - 10e²) + (-12e⁵ + 4e⁴ + 14e²)

1. (9b⁵ - 6 + 3b⁴) - (b⁴ - 7b⁵ - 3)
2. (k⁴ - 1 - 3k³) + (-5k⁴ + 6k³ - 8k²)
3. (-10k² + 7k + 6k⁴) + (-14 - 4k⁴ - 14k)
4. (-7n² + 8n - 4) - (-11n + 2 - 14n²)
5. (14p⁴ + 11p² - 9p⁵) - (-14 + 5p⁵ - 11p²)
6. (8k + k³ - 6) - (-10k + 7 - 2k²)
7. (-9v² - 8u) + (-2uv - 2u² + v²) + (-v² + 4uv)
8. (4x² + 7x³y²) - (-6x² - 7x³y⁴ - 4x) - (10x + 9x²)
9. (-5u³v⁴ + 9u) + (-5u³v⁴ - 8u + 8u³v²) + (-8u⁴v² + 8u³v⁴)
10. (-9xy³ - 9x⁴y³) + (3xy³ + 7y⁴ - 8x⁴y⁴) + (3x⁴y³ + 2xy³)
11. (y³ + 7x⁴y³) + (-10x⁴y³ + 6y³ + 4x⁴y⁴) - (x⁴y³ + 6x⁴y⁴)

Explanation:

Let's solve problem 21: \((k^4 - 1 - 3k^3) + (-5k^4 + 6k^3 - 8k^2)\)

Step 1: Identify like terms

Like terms are terms with the same variable and exponent. So we have:

• \(k^4\) terms: \(k^4\) and \(-5k^4\)
• \(k^3\) terms: \(-3k^3\) and \(6k^3\)
• \(k^2\) term: \(-8k^2\)
• Constant term: \(-1\)

Step 2: Combine \(k^4\) terms

\(k^4 + (-5k^4) = k^4 - 5k^4 = -4k^4\)

Step 3: Combine \(k^3\) terms

\(-3k^3 + 6k^3 = 3k^3\)

Step 4: Bring down remaining terms

We have \(-8k^2\) and \(-1\)

Step 5: Combine all terms

Putting it all together: \(-4k^4 + 3k^3 - 8k^2 - 1\)

Answer:

\(-4k^4 + 3k^3 - 8k^2 - 1\)