Select the correct answer.

Which sum or difference is modeled by the algebra tiles?

A. (-x2 + 2x + 3) − (x2 − 2x − 1) = -2x2 + 2

B. (-x2 + 2x + 3) − (-x2 + 2x + 1) = -2x2 + 2

C. (-x2 + 2x + 3) + (-x2 + 2x + 1) = -2x2 + 2

D. (-x2 + 2x + 3) + (-x2 − 2x − 1) = -2x2 + 2

Question

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nonsibi nonsibi · Answer 1 · 2019-12-31T03:28:58+01:00

The only answer choice that produces -2x²+2 is D.

Because (-x²+2x+3)+(-x²-2x-1) = -x²+2x+3-x²-2x-1 = -2x²+2

answer: D

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MrRoyal MrRoyal · Answer 2 · 2022-03-10T14:42:16+01:00

The algebraic sum modelled by the tiles is (d)[tex](-x^2 + 2x + 3) + (-x^2 - 2x - 1) = -2x2 + 2[/tex]

From the figure, we have the result of the algebraic tiles to be:

[tex]-x^2 - x^2 + 1 + 1[/tex]

This gives

[tex]-2x^2 + 2[/tex]

Next, we test the options (A) through (D)

Option A

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

Open the brackets

[tex]-x^2 + 2x + 3 - x^2 + 2x + 1 = -2x^2 + 2[/tex]

Evaluate the like terms

[tex]-2x^2 + 4x + 4 \ne -2x^2 + 2[/tex]

When the same is applied to the remaining options, we have:

Option B.

[tex](-x^2 + 2x + 3) - (-x^2 + 2x + 1) \ne -2x^2 + 2[/tex]

Option C

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

Option D

[tex](-x^2 + 2x + 3) + (-x^2 - 2x - 1) = -2x2 + 2[/tex]

Hence, the algebraic sum modelled by the tiles is (d) [tex](-x^2 + 2x + 3) + (-x^2 - 2x - 1) = -2x2 + 2[/tex]