Final answer:
The products that result in a difference of squares or a perfect square trinomial are: (5x+3)(5x-3), (4x-6)(x+8), and (x-9)(x-9). To determine if a product is a difference of squares or a perfect square trinomial, check if it can be written as the square of a binomial.
Step-by-step explanation:
The products that result in a difference of squares or a perfect square trinomial are:
- (5x+3)(5x-3)
- (4x-6)(x+8)
- (x-9)(x-9)
To determine if a product is a difference of squares or a perfect square trinomial, you need to check if the expression can be written as the square of a binomial. For a difference of squares, the expression should have the form (a-b)(a+b), where a and b are terms. For a perfect square trinomial, the expression should have the form (a+b)² or (a-b)². In the given options, the first expression can be written as (5x)² - (3)², the second expression can be written as (2x)² - (1)², and the third expression is already in the form of a perfect square trinomial.