Question

He variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x – 3. What is AB – C2 in simplest form?

Answer 1

`A=x^2\\B=3x+2\\C=x-3\\\\AB-C^2\\\text{Substitute:}\\\\(x^2)(3x+2)-(x-3)^2\\\\\text{Use distributive property}\ a(b+c)=ab+ac\\\text{and}\ (a-b)^2=a^2-2ab+b^2:\\\\(x^2)(3x)+(x^2)(2)-[x^2-(2)(x)(3)+3^2]\\\\=3x^3+2x^2-x^2+6x-9\\\\=\boxed{3x^3+x^2+6x-9}`