Final answer:
The simplified form of the expression (x³ + 2x²) - (6x - 4x² + 2x³) is -x³ + 6x² - 6x, achieved by distributing the negative sign and combining like terms.
Step-by-step explanation:
To solve the expression (x³ + 2x²) - (6x - 4x² + 2x³), you need to distribute the negative sign in the second parenthesis to every term inside it and then combine like terms. Here are the steps:
- Distribute the negative sign: (x³ + 2x²) - 6x + 4x² - 2x³
- Combine like terms: (x³ - 2x³) + (2x² + 4x²) - 6x
- Simplify: -x³ + 6x² - 6x
So the simplified form of the given expression is -x³ + 6x² - 6x.
To solve the expression (x³ + 2x²) - (6x - 4x² + 2x³), we combine like terms by adding or subtracting the coefficients of x raised to the same power. This gives us (x³ + 2x² - 6x + 4x² - 2x³). Next, we simplify the expression by rearranging the terms in descending order of the powers of x: -2x³ + x³ + 4x² + 2x² - 6x.
Combining like terms again, we get -x³ + 6x² - 6x. Therefore, the simplified expression is -x³ + 6x² - 6x.