Question

the variables a, b, and c represent polynomials where ( a = x^2 ), ( b = 3x + 2 ), and ( c = x - 3 ). what is ( ab - c^2 ) in simplest form?
( \bigcirc 3x^3 + 2x^2 - x + 3 )
( \bigcirc 3x^3 + 2x^2 - x - 3 )
( \bigcirc 3x^3 + x^2 - 6x + 9 )
( \bigcirc 3x^3 + x^2 + 6x - 9 )

Explanation:

Step1: Calculate $AB$

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

Step2: Calculate $C^2$

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

Step3: Compute $AB - C^2$

$AB - C^2 = (3x^3 + 2x^2) - (x^2 - 6x + 9) = 3x^3 + 2x^2 - x^2 + 6x - 9 = 3x^3 + x^2 + 6x - 9$

Answer:

$3x^3 + x^2 + 6x - 9$ (the fourth option)