Answer:
[tex]AB-C^2[/tex] in simplest form:
[tex]3x^3+x^2+6x-9[/tex]
Step-by-step explanation:
The distributive property says that:
[tex]a \cdot (b+c) =a\cdot b+ a\cdot c[/tex]
Given that:
The variables A, B, and C represent polynomials
Where,
[tex]A = x^2[/tex]
[tex]B = 3x+2[/tex]
[tex]C = x-3[/tex]
We have to find the [tex]AB-C^2[/tex]
then;
[tex]AB-C^2[/tex] =[tex](x^2)(3x+2)-(x-3)^2[/tex]
Apply the distributive property :
[tex](3x^3+2x^2)-(x-3)^2[/tex]
⇒[tex]3x^3+2x^2-(x^2+9-6x)[/tex]
Remove the bracket, we have;
[tex]3x^3+2x^2-x^2-9+6x[/tex]
Combine like terms;
[tex]3x^3+x^2+6x-9[/tex]
Therefore, [tex]AB-C^2[/tex] in simplest form: [tex]3x^3+x^2+6x-9[/tex]
