Question

(Constructed Response) Determine whether the binomial, 9x² - 49, is a difference of

Answer 1

Answer: It is a difference of two squares, and it factors to (3x-7)(3x+7)

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Explanation:

We can write the 9x^2 as (3x)^2 since

(3x)^2 = (3x)*(3x) = (3*3)*(x*x) = 9x^2

The 49 can be written as 7^2 because 7^2 = 7*7 = 49.

This means 9x^2 - 49 is the same as (3x)^2 - 7^2. We have a difference of two squares.

The difference of squares factoring rule is

a^2 - b^2 = (a-b)(a+b)

which we have a = 3x and b = 7 in this case

So,

a^2 - b^2 = (a-b)(a+b)

(3x)^2 - 7^2 = (3x-7)(3x+7)

9x^2 - 49 = (3x-7)(3x+7)

Side note: This is the same as (3x+7)(3x-7). We can multiply two numbers in any order.