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Which sum or difference is modeled by the algebra tiles?

A. [tex]\((-x^2 + 2x + 3) - (x^2 - 2x - 1) = -2x^2 + 2\)[/tex]

B. [tex]\((x^2 + 2x + 3) - (-x^2 + 2x + 1) = -2x^2 + 2\)[/tex]

C. [tex]\((x^2 + 2x + 3) + (-x^2 + 2x + 1) = -2x^2 + 2\)[/tex]

D. [tex]\((-x^2 + 2x + 3) + (-x^2 - 2x - 1) = -2x^2 + 2\)[/tex]

Sagot :

GinnyAnswer
To solve the problem, we need to determine which option correctly describes the difference or sum of the given polynomials based on the result [tex]\(-2x^2 + 4x + 4\)[/tex].

Let's break down each option:

### Option A: [tex]\((-x^2 + 2x + 3) - (x^2 - 2x - 1)\)[/tex]

1. Write the expression:
[tex]\[ (-x^2 + 2x + 3) - (x^2 - 2x - 1) \][/tex]
2. Distribute the negative sign:
[tex]\[ -x^2 + 2x + 3 - x^2 + 2x + 1 \][/tex]
3. Combine like terms:
[tex]\[ -2x^2 + 4x + 4 \][/tex]

The calculations match the result [tex]\(-2x^2 + 4x + 4\)[/tex].

### Option B: [tex]\((x^2 + 2x + 3) - (-x^2 + 2x + 1)\)[/tex]

1. Write the expression:
[tex]\[ (x^2 + 2x + 3) - (-x^2 + 2x + 1) \][/tex]
2. Distribute the negative sign:
[tex]\[ x^2 + 2x + 3 + x^2 - 2x - 1 \][/tex]
3. Combine like terms:
[tex]\[ 2x^2 + 2 \][/tex]

This does not match the result [tex]\(-2x^2 + 4x + 4\)[/tex], so option B is incorrect.

### Option C: [tex]\((x^2 + 2x + 3) + (-x^2 + 2x + 1)\)[/tex]

1. Write the expression:
[tex]\[ (x^2 + 2x + 3) + (-x^2 + 2x + 1) \][/tex]
2. Combine like terms:
[tex]\[ x^2 - x^2 + 2x + 2x + 3 + 1 \][/tex]
3. Combine:
[tex]\[ 4x + 4 \][/tex]

This does not match the result [tex]\(-2x^2 + 4x + 4\)[/tex], so option C is incorrect.

### Option D: [tex]\((-x^2 + 2x + 3) + (-x^2 - 2x - 1)\)[/tex]

1. Write the expression:
[tex]\[ (-x^2 + 2x + 3) + (-x^2 - 2x - 1) \][/tex]
2. Combine like terms:
[tex]\[ -x^2 - x^2 + 2x - 2x + 3 - 1 \][/tex]
3. Combine:
[tex]\[ -2x^2 + 2 \][/tex]

This does not match the result [tex]\(-2x^2 + 4x + 4\)[/tex], so option D is incorrect.

### Conclusion:
Upon review, the only option that matches the result [tex]\(-2x^2 + 4x + 4\)[/tex] is Option A:
[tex]\[ (-x^2 + 2x + 3) - (x^2 - 2x - 1) = -2x^2 + 4x + 4 \][/tex]

Therefore, the correct answer is:
A. (-x² + 2x + 3) - (x² - 2x - 1) = -2x² + 4x + 4
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