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Add: 4x² - 7xy + 4y² -3, 5+6y²-8xy+x² and 6-2xy +2x²-5y²?
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Add: 4x² - 7xy + 4y² -3, 5+6y²-8xy+x² and 6-2xy +2x²-5y²?


Addition of Polynomials:

When adding polynomials, we combine like terms by adding the coefficients of the same variables raised to the same powers.

  • First Polynomial: 4x² - 7xy + 4y² - 3
  • Second Polynomial: 5 + 6y² - 8xy + x²
  • Third Polynomial: 6 - 2xy + 2x² - 5y²


Step 1: Combine Like Terms

  • x² Terms: 4x² + x² + 2x² = 7x²
  • xy Terms: -7xy - 8xy - 2xy = -17xy
  • y² Terms: 4y² + 6y² - 5y² = 5y²
  • Constants: -3 + 5 + 6 = 8


Step 2: Combine the Results

Putting all the combined terms together, we get:

7x² - 17xy + 5y² + 8

Final Answer:

The sum of the three polynomials is 7x² - 17xy + 5y² + 8.

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Add: 4x² - 7xy + 4y² -3, 5+6y²-8xy+x² and 6-2xy +2x²-5y²?
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