Final answer:
To multiply -5x²(6x - 1), distribute -5x² across the terms in the parentheses to get -30x³ + 5x². This utilizes the distributive property and multiplication rules for signs.
Step-by-step explanation:
To multiply the polynomials -5x²(6x - 1) using the distributive property, you distribute -5x² across the terms inside the parentheses by multiplying -5x² by each term individually. Here are the steps:
- Multiply -5x² by 6x to get: -30x³.
- Multiply -5x² by -1 to get: +5x².
Combine the products from steps 1 and 2 to obtain the simplified polynomial expression: -30x³ + 5x².
This method follows the basic multiplication rules for signs: the product of two numbers with the same sign is positive, and the product of two numbers with opposite signs is negative.
To use the distributive property to multiply the polynomials -5x² and (6x - 1), you need to distribute -5x² to each term inside the parentheses:
-5x²(6x) - 5x²(-1) = -30x³ + 5x²
The simplified polynomial expression after distributing is -30x³ + 5x².