[tex]A = x^2[/tex]
[tex]B = 3x + 2[/tex]
[tex]C = x - 3[/tex]
We are trying to find [tex]AB - C^2[/tex], so let's simply substitute in the information we know for our variables and simplify:
[tex]AB - C^2 = (x^2)(3x + 2) - (x - 3)^2[/tex]
[tex]3x^3 + 2x^2 - (x - 3)^2[/tex]
- Apply the Distributive Property
[tex]3x^3 + 2x^2 - (x^2 - 6x + 9)[/tex]
- Simplify the last term through FOIL
[tex]3x^3 + x^2 + 6x - 9[/tex]
Our answer is 3x³ + x² + 6x - 9.
