Subtract (5x²-6x+4) from the sum of (-3x²+3x+1) and 2x²-5x+7)
just working with the x² terms, we have
-3+2-5 = -6x²
do the x's and constants the same way.
To subtract (5x² - 6x + 4) from the sum of (-3x² + 3x + 1) and (2x² - 5x + 7), follow these steps:
1. Add the two given expressions: -3x² + 3x + 1 + 2x² - 5x + 7.
This simplifies to: -3x² + 2x² + 3x - 5x + 1 + 7.
Combining like terms, we get: -x² - 2x + 8.
2. Now subtract (5x² - 6x + 4) from the result obtained in step 1: (-x² - 2x + 8) - (5x² - 6x + 4).
To do this, we need to distribute the negative sign on the second expression:
-1 * 5x² = -5x²
-1 * -6x = +6x
-1 * 4 = -4
Now we have:
(-x² - 2x + 8) - (5x² - 6x + 4)
= -x² - 2x + 8 - 5x² + 6x - 4
3. Combine like terms:
= -x² - 5x² - 2x + 6x + 8 - 4
= -6x² + 4x + 4
So the final result is -6x² + 4x + 4.
To subtract (5x²-6x+4) from the sum of (-3x²+3x+1) and (2x²-5x+7), we need to first find the sum of (-3x²+3x+1) and (2x²-5x+7), and then subtract (5x²-6x+4) from the obtained sum.
Let's find the sum of (-3x²+3x+1) and (2x²-5x+7):
(-3x²+3x+1) + (2x²-5x+7)
Combine like terms by adding the coefficients of the same degree terms:
(-3x² + 2x²) + (3x - 5x) + (1 + 7)
Simplify each group of like terms:
(-1x²) + (-2x) + (8)
Now, we have the sum of (-3x²+3x+1) and (2x²-5x+7) as: -x² - 2x + 8.
Finally, we can subtract (5x²-6x+4) from the obtained sum:
(-x² - 2x + 8) - (5x² - 6x + 4)
When subtracting, distribute the negative sign to each term inside the parentheses:
-x² - 2x + 8 - 5x² + 6x - 4
Combine like terms by adding or subtracting the coefficients of the same degree terms:
(-x² - 5x²) + (-2x + 6x) + (8 - 4)
Simplify each group of like terms:
-6x² + 4x + 4
Therefore, subtracting (5x²-6x+4) from the sum of (-3x²+3x+1) and (2x²-5x+7) gives us the final answer of -6x² + 4x + 4.