the variables a, b, and c represent polynomials where a = x², b = 3x + 2, and c = x - 3. what is ab - c² in…

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?\n3x³ + 2x² - x + 3\n3x³ + 2x² - x - 3\n3x³ + x² - 6x + 9\n3x³ + x² + 6x - 9

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?\n3x³ + 2x² - x + 3\n3x³ + 2x² - x - 3\n3x³ + x² - 6x + 9\n3x³ + x² + 6x - 9

Answer

Answer:

D. $3x^{3}+x^{2}+6x - 9$

Explanation:

Step1: Calculer le produit $AB$

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

Step2: Calculer le carré de $C$

$C^{2}=(x - 3)^{2}=x^{2}-6x + 9$ (en utilisant la formule $(a - b)^{2}=a^{2}-2ab + b^{2}$ avec $a = x$ et $b = 3$)

Step3: Calculer $AB - C^{2}$

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