Question

The 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

$A = x^2$

$B = 3x + 2$

$C = x - 3$

We are trying to find $AB - C^2$, so let's simply substitute in the information we know for our variables and simplify:

$AB - C^2 = (x^2)(3x + 2) - (x - 3)^2$

• Substitute

$3x^3 + 2x^2 - (x - 3)^2$

• Apply the Distributive Property

$3x^3 + 2x^2 - (x^2 - 6x + 9)$

• Simplify the last term through FOIL

$3x^3 + x^2 + 6x - 9$

• Combine like terms

Our answer is 3x³ + x² + 6x - 9.