To multiply and simplify the expression (a-2)(8a^2-5a+3), you need to use the distributive property. This means you will multiply each term in the first parenthesis by each term in the second parenthesis.
Here's how you can do it step by step:
1. Multiply a by each term in the second parenthesis:
a * 8a^2 = 8a^3
a * (-5a) = -5a^2
a * 3 = 3a
2. Multiply -2 by each term in the second parenthesis:
-2 * 8a^2 = -16a^2
-2 * (-5a) = 10a
-2 * 3 = -6
3. Now, add all the results together:
8a^3 - 5a^2 + 3a - 16a^2 + 10a - 6
4. Combine like terms:
8a^3 - 21a^2 + 13a - 6
Therefore, the simplified expression after multiplying and simplifying (a-2)(8a^2-5a+3) is 8a^3 - 21a^2 + 13a - 6.
