A. 9x^2 − 25.
Sure, let's solve the question together step-by-step!
The product of two binomials `(a - b)` and `(a + b)` can be calculated using the formula `a^2 - b^2`. This is known as the difference of squares formula, which is an important algebraic identity.
First, let's identify `a` and `b` in our case. Here, `a` is `3x` and `b` is `5`.
For `(3x - 5)` and `(3x + 5)`, using the formula, let's substitute `a` and `b` to get:
`(3x)^2 - 5^2`
Next, we simplify `(3x)^2` to `9x^2` – remember when raising a product to a power, each part of the product is raised to that power – and `5^2` to `25`.
So, the product of `(3x - 5)` and `(3x + 5)` simplifies to:
`9x^2 - 25`
So, looking at the given options, we can say that the product of (3x - 5) and (3x + 5) is:
A. 9x^2 − 25.