when (2x-3)^2 is subtracted from 5x^2, what is the result in simplest form

Question

cant figure this out

Answer 1

"when (2x-3)^2 is subtracted from 5x^2"

 

So, in other words, when this happens:

 

5x² - (2x-3)²

 

"what is the result in simplest form" -> Well we need to foil things out, combine like terms, and then simplify if possible

 

5x² - (2x-3)(2x-3)

 

5x² - (4x² -6x -6x + 9)

 

5x² - (4x² -12x + 9)

 

5x² - 4x² + 12x - 9

 

x² + 12x - 9

 

 

So here we've foiled/distributed everything, and combined like terms as much as possible. Now we have a simple quadratic equation. Only way we can simplify it further is if it is factorable. (x-a)(x-b) = x² +12x - 9? There is no way to solve that with integers so this quadratic equation is in simplest form.