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

AB - C2 = (x2)(3x + 2) - (x-3)2
AB - C2 = 3x3 + 2x2 - (x2 -6x +9)
AB - C2 = = 3x3 + 2x2 - x2 + 6x - 9
AB - C2 = = 3x3 + x2 + 6x - 9

Answer 2

Answer:

$AB-C^2$ in simplest form:

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

Step-by-step explanation:

The distributive property says that:

$a \cdot (b+c) =a\cdot b+ a\cdot c$

Given that:

The variables A, B, and C represent polynomials

Where,

$A = x^2$

$B = 3x+2$

$C = x-3$

We have to find the $AB-C^2$

then;

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

Apply the distributive property :

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

⇒$3x^3+2x^2-(x^2+9-6x)$

Remove the bracket, we have;

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

Combine like terms;

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

Therefore, $AB-C^2$ in simplest form: $3x^3+x^2+6x-9$