## 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? 3×3 + 2×2 – x +

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

in progress 0
2 weeks 2021-11-20T21:58:46+00:00 2 Answers 0

AB – C² = 3x³ + x² + 6x – 9 ⇒ last answer

Step-by-step explanation:

* Lets study the problem to solve it

– The variables are:

# A = x²

# B = 3x + 2

# C = x – 3

* At first lets find AB

∵ A = x² and B = 3x + 2

∴ AB = x²(3x + 2)

∵ x² × 3x = 3x³ ⇒ same base so we added the power

∵ x² × 2 = 2x² ⇒ coefficient of x² is 1 multiplied by 2

∴ AB = 3x³ + 2x²

* At second find C²

∵ C = x – 3

∴ C² = (x – 3)²

– To solve bracket to the power of 2 use this rule:

# square the first term + 1st term × 2nd term × 2 + square the 2nd term

∴ (x – 3)² = (x²) + (x) (-3) (2) + (-3)² = x² – 6x + 9

∴ C² = x² – 6x + 9

* Now lets find AB – C²

∵ AB – C² = 3x³ + 2x² – (x² – 6x + 9) ⇒ multiply the bracket by -ve sign

∵ -ve × -ve = +ve

∵ -ve × +ve = -ve

∴ AB – C² = 3x³ + 2x² – x² + 6x – 9 ⇒ Add the like terms

∴ AB – C² = 3x³ + x² + 6x – 9

* AB – C² = 3x³ + x² + 6x – 9