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77julia77 [94]
3 years ago
14

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
2 answers:
Bingel [31]3 years ago
6 0
AB - C2 = (x2)(3x + 2) - (x-3)2
AB - C2 = 3x3 + 2x2 - (x2 -6x +9)
AB - C2 = = 3x3 + 2x2 - x2 + 6x - 9
AB - C2 = = 3x3 + x2 + 6x - 9
MArishka [77]3 years ago
4 0

Answer:

AB-C^2 in simplest form:

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

Step-by-step explanation:

The distributive property says that:

a \cdot (b+c) =a\cdot b+ a\cdot c

Given that:

The variables A, B, and C represent polynomials

Where,

A = x^2

B = 3x+2

C = x-3

We have to find the AB-C^2

then;

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

Apply the distributive property :

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

⇒3x^3+2x^2-(x^2+9-6x)

Remove the bracket, we have;

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

Combine like terms;

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

Therefore, AB-C^2 in simplest form: 3x^3+x^2+6x-9

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