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?
3x3 + 2x2 – x + 3
3x3 + 2x2 – x – 3
3x3 + x2 – 6x + 9
3x3 + x2 + 6x – 9

Answer 1

A = x²,
B = 3x + 2,
C = x – 3

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

Answer 2

The simplest form of $\rm AB-C^2$ will be $3x^3+x^2+6x-9$ and it can be determine by using arithmetic operations.

Given :

• $\rm A = x^2$

• $\rm B = 3x +2$

• $\rm C = x-3$

The following steps can be used to find the simplest form of $\rm (AB-C^2)$ :

Step 1 - Multiply A with B.

$\rm A\times B=x^2\times(3x+2)$

$\rm A\times B=3x^3+2x^2$ ----- (1)

Step 2 - Now, Square the value of C.

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

Step 3 - Subtract $\rm C^2$ from both the side of equation (1).

$\rm A\times B-C^2 = 3x^3+2x^2-x^2+6x-9$

$\rm AB - C^2= 3x^3+x^2+6x-9$

Therefore the correct option is D).

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