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

`AB-C^2` in simplest form:

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

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`