From the sum of 3x² + 2y², -x² -4y² + 2xy and 6xy + 2x² - 3y²,
subtract - 5x² + 2y² - 3xy.
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First we add:
3x² + 2y², - x² - 4y² + 2xy and 6xy + 2x² - 3y².
3x² + 2y², - x² - 4y² + 2xy + 6xy + 2x² - 3y²
= (3x² - x² + 2x²) + (2y² - 4y² - 3y²) + (2xy + 6xy)
= 4x² - 5y² + 8xy
Now, we subtract:
- 5x² + 2y² - 3xy from 4x² - 5y² + 8xy
(4x² - 5y² + 8xy) - (- 5x² + 2y² - 3xy)
= 4x² - 5y² + 8xy + - 5x² + 2y² - 3xy
= (4x² + 5x²) + (-5y² - 2y²) + (8xy + 3xy)
= 9x² - 7y² + 11xy
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