Sure, let's proceed step by step:
Step 1: Write down the given expressions
The given expressions are:
1. 3x² - 8x + 1
2. -x² + 4
3. 6x³ - x
Step 2: Subtract the second expression from the first
To do this, we change the signs of each of the terms in the second expression and then add the results to the corresponding terms in the first expression:
(3x² - 8x + 1) - (-x² + 4) becomes:
3x² - (-x²) - 8x - (-0) + 1 - 4
Solve for each operation:
4x² - 8x - 3
Step 3: Multiply the result from Step 2 by expression 3
To perform this operation, we multiply each term in the result from Step 2 by each term in the third expression:
(4x² - 8x - 3) * (6x³ - x)
This leads us to:
24x⁵ - 4x⁴ - 48x³ + 8x² - 18x³ + 3x
Step 4: Combine like terms and simplify the expression
Combining the terms with the same powers of x and simplifying gives us:
24x⁵ - 4x⁴ - 66x³ + 8x² + 3x
So, (3x² - 8x + 1) - (-x² + 4) * (6x³ - x) simplifies to 24x⁵ - 48x⁴ - 22x³ + 8x² + 3x when written in the standard form.