Final answer:
The expression ((-4x^7 + 7x^9 - 3 - 2x^8) - (1 - 9x^8 + 2x^9 - 2x^7)) simplifies to 5x^9 + 7x^8 - 2x^7 - 4 by combining like terms and changing signs of the terms in the second parentheses.
Step-by-step explanation:
The student has asked to simplify the expression ((-4x^7 + 7x^9 - 3 - 2x^8) - (1 - 9x^8 + 2x^9 - 2x^7)). To do this, we combine like terms by subtracting the contents of the second set of parentheses from the first. This means changing the signs of the terms inside the second set of parentheses before adding them to the first.
Here is the step-by-step solution:
- Step 1: Remove parentheses and change signs: -4x^7 + 7x^9 - 3 - 2x^8 - 1 + 9x^8 - 2x^9 + 2x^7
- Step 2: Combine like terms: (7x^9 - 2x^9) + (-2x^8 + 9x^8) + (-4x^7 + 2x^7) - 3 - 1
- Step 3: Simplify: 5x^9 + 7x^8 - 2x^7 - 4
The simplified expression is 5x^9 + 7x^8 - 2x^7 - 4.