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Which of the following is the product of (3x − 5) and (3x + 5)?

A. 9x^2 − 25
B. 9x^2 − 30x − 25
C. 9x − 10
D. 9x^2 + 25

1 Answer

6 votes

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.

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