How do you factor 9xy^2 - 25?

1 Answer
Jun 3, 2015

If you look at 9 and 25, they are both perfect squares. So I suppose if you wanted to factor this, you can call this equation a "difference of two squares". Let's take this for example:

(x^("*"A)-2)(x^("*"B)+2) = (x-2)(x+2) = x^2 cancel(+ 2x - 2x) - 4 = x^2 - 4

where x^("*A") and x^("*B") are just labels to distinguish the first x from the second x.

Notice that x^("*"A)x^("*B") = x^2 and -2*2 = -(2*2) = -(4). Similarly, we can work backwards.

First, we can take the square root of 9xy^2 to get 3x^(1/2)y. Then, we can take the positive square root of |25| to get 5. Afterwards we can just follow the example above to get:

(3x^(1/2)y - 5)(3x^(1/2)y + 5)

or

(3sqrtxy - 5)(3sqrtxy + 5)

Normally though, it's unusual to put square roots in factored answers.