Final answer:
To simplify the expression (9x³) (2x-10), the associative property doesn't apply; instead, use the distributive property to multiply across the terms, resulting in 18x⁴ - 90x³.
Step-by-step explanation:
The student is asking how to use the associative property to simplify the expression (9x³) (2x-10). The associative property in mathematics allows us to group numbers in an algebraic expression in different ways without changing the result of the expression. In this case, the associative property isn't necessary to simplify the expression because there is nothing to associate differently; the expression only involves multiplication that has to be carried out. So, we need to expand the expression by multiplying 9x³ with each term in the binomial (2x-10).
To simplify, use the distributive property:
- Multiply 9x³ by 2x to get 18x⁴
- Multiply 9x³ by -10 to get -90x³
This gives us the simplified form of the expression:
18x⁴ - 90x³.