Final answer:
The expression (3x - 5)(3x - 5) results in a perfect square trinomial. It's the squaring of a binomial which leads to an identical binomial multiplication, producing a trinomial where the first and last terms are squares of the original binomial terms and the middle term is twice the product of the original terms.
Step-by-step explanation:
Perfect Square Trinomial Creation-
The expression that will result in a perfect square trinomial is (3x – 5)(3x – 5). When you multiply this expression, you're essentially squaring the binomial 3x – 5, which is the definition of creating a perfect square trinomial. A perfect square trinomial is one that can be factored into an identical binomial multiplication: (ax – b)(ax – b) = a²x² – 2abx + b².
To demonstrate: (3x – 5)2 = (3x – 5)(3x – 5) = 9x2 – 15x – 15x + 25 = 9x2 – 30x + 25.
In contrast:
- (3x – 5)(5 – 3x) results in a difference of squares.
- (3x – 5)(3x + 5) also results in a difference of squares.
- (3x – 5)(–3x – 5) results in the expansion of a product of differing terms.