Final answer:
Expressions are simplified by combining like terms, applying the distributive property, and performing arithmetic operations. The results are 3x³ + 3x² + 2x - 8, 3y² + 8y + 1, 6k² + 2k - 30, and 12m³ - 22m² + 18m - 4.
Step-by-step explanation:
We will simplify each expression step-by-step.
- (3x³ + 2x² - 3x - 2) + (x² + 5x - 6): Combine like terms by adding coefficients for the same powers of x. Simplified, this expression is 3x³ + 3x² + 2x - 8.
- (12y² + 5y - 6) - (9y² - 3y - 4) + 11: Distribute the negative sign through the second parentheses and then combine like terms. The simplified expression is 3y² + 8y + 1.
- (2k - 5)(3k + 6): Apply the distributive property, also known as the FOIL method, to multiply each term in the first polynomial by each term in the second polynomial. The result is 6k² + 2k - 30.
- (6m - 2)(2m² - 3m + 2): Again, use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. The expanded form is 12m³ - 18m² + 12m - 4m² + 6m - 4, which simplifies to 12m³ - 22m² + 18m - 4.
Always eliminate terms wherever possible to simplify the algebra and check the answer to ensure it is reasonable.