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docker41 [41]
3 years ago
11

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?

Mathematics
1 answer:
laila [671]3 years ago
4 0

A = x^2

B = 3x + 2

C = x - 3


We are trying to find AB - C^2, so let's simply substitute in the information we know for our variables and simplify:

AB - C^2 = (x^2)(3x + 2) - (x - 3)^2

  • Substitute

3x^3 + 2x^2 - (x - 3)^2

  • Apply the Distributive Property

3x^3 + 2x^2 - (x^2 - 6x + 9)

  • Simplify the last term through FOIL

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

  • Combine like terms

Our answer is 3x³ + x² + 6x - 9.

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