Final answer:
The expression (6x(x² - 4x + 8)) is simplified by distributing 6x across each term inside the parentheses, resulting in (6x³ - 24x² + 48x), which matches option (a).
Step-by-step explanation:
To simplify the expression (6x(x² - 4x + 8)), you distribute the 6x across the terms in the parentheses, which involves multiplying 6x by each term inside the parentheses. The process goes as follows:
- 6x * x² = 6x³
- 6x * (-4x) = -24x²
- 6x * 8 = 48x
Thus, the simplified expression is (6x³ - 24x² + 48x), which corresponds to option (a).
When simplifying algebraic expressions, it is important to carefully apply the distributive property and combine like terms when possible. However, in this case, there are no like terms to combine after the initial multiplication.
Always remember to check your answer to ensure it is reasonable and there are no terms left to simplify.