Final answer:
To subtract the sum of two expressions from another expression, distribute the negative sign to each term in the sum and then combine like terms. Sum of the two expressions from the third expression is x² - 2x + 3.
Step-by-step explanation:
To subtract the sum of 2x-x²+5 and 7x²-4x-3 from 7x²-4x+5, we can distribute the negative sign to each term in the sum and then combine like terms. The subtraction can be done by changing the signs of each term in the sum and then adding the resulting expressions.
So, 7x²-4x+5 - (2x-x²+5 + 7x²-4x-3) becomes 7x²-4x+5 - 2x+x²-5-7x²+4x+3.
Combining like terms, we get -3x² + 6.
First, we need to find the sum of 2x - x² + 5 and 7x² - 4x - 3 before we can substact it from 7x² - 4x + 5. To do this, we combine like terms:
(2x - x² + 5) + (7x² - 4x - 3) = (-x² + 7x²) + (2x - 4x) + (5 - 3) = 6x² - 2x + 2.
Now, we subtract the sum from 7x² - 4x + 5, meaning we perform the operation ((7x² - 4x + 5) - (6x² - 2x + 2)):
7x² - 4x + 5 - (6x² - 2x + 2) = 7x² - 4x + 5 - 6x² + 2x - 2 = (7x² - 6x²) + (-4x + 2x) + (5 - 2) = x² - 2x + 3.
The final result of subtracting the sum of the two expressions from the third expression is x² - 2x + 3.