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To subtract the second expression from the first, we must distribute the negative sign through the second expression and then combine like terms.
(8X^2 - 6X - 3) - (4X^2 - 5X + 4)
= 8X^2 - 6X - 3 - 4X^2 + 5X - 4
= 8X^2 - 4X^2 - 6X + 5X - 3 - 4
= 4X^2 - X - 7
So, (8X^2 - 6X - 3) - (4X^2 - 5X + 4) simplifies to 4X^2 - X - 7.