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Adding and Subtracting Polynomials Practice

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Sure! Here are some practice problems for adding and subtracting polynomials, along with explanations on how to solve them.

Practice Problems

  1. \( (3x^2 + 4x - 5) + (2x^2 - 3x + 7) \)
  2. \( (5a^3 - 2a + 1) - (3a^3 + a - 4) \)
  3. \( (6m^2 + 3m - 8) + (4m^2 - 6m + 2) \)
  4. \( (x^4 - 2x^2 + 7) - (3x^4 + x^2 - 1) \)
  5. \( (7p^3 + 5p^2 - 2p) + (2p^3 - 4p^2 + 3) \)

Instructions to Solve

  1. Identify Like Terms: Like terms are terms that have the same variable raised to the same power.

  2. Combine Like Terms: Add or subtract the coefficients of like terms.

  3. Write the Final Answer: Make sure to write the final answer in standard form, which means the terms should be arranged in descending order of their degree.

Solutions

  1. Solution for \( (3x^2 + 4x - 5) + (2x^2 - 3x + 7) \): \[ (3x^2 + 2x^2) + (4x - 3x) + (-5 + 7) = 5x^2 + x + 2 \]

  2. Solution for \( (5a^3 - 2a + 1) - (3a^3 + a - 4) \): \[ (5a^3 - 3a^3) + (-2a - a) + (1 + 4) = 2a^3 - 3a + 5 \]

  3. Solution for \( (6m^2 + 3m - 8) + (4m^2 - 6m + 2) \): \[ (6m^2 + 4m^2) + (3m - 6m) + (-8 + 2) = 10m^2 - 3m - 6 \]

  4. Solution for \( (x^4 - 2x^2 + 7) - (3x^4 + x^2 - 1) \): \[ (x^4 - 3x^4) + (-2x^2 - x^2) + (7 + 1) = -2x^4 - 3x^2 + 8 \]

  5. Solution for \( (7p^3 + 5p^2 - 2p) + (2p^3 - 4p^2 + 3) \): \[ (7p^3 + 2p^3) + (5p^2 - 4p^2) + (-2p + 0) + 3 = 9p^3 + p^2 - 2p + 3 \]

Feel free to try these problems on your own before looking at the solutions! Let me know if you need further assistance or explanations!