Question

which sum or difference is modeled by the algebra tiles? (image of algebra tiles: two -x² tiles, four -x tiles, four +1 tiles, one -1 tile) a. (-x² - 2x + 4) - (x² + 2x + 1) = -2x² - 4x + 3 b. (-x² - 2x + 4) + (-x² - 2x + 1) = -2x² - 4x + 3 c. (-x² - 2x + 4) - (x² - 2x - 1) = -2x² - 4x + 3 d. (-x² - 2x + 4) + (-x² + 2x + 1) = -2x² - 4x + 3

Explanation:

Step1: Count algebra tiles

Red tiles: $-x^2$ (2), $-x$ (4), $-1$ (1); Blue tiles: $+1$ (4). Total: $-2x^2 -4x +3$.

Step2: Check option B

Left term: $-x^2 -2x +4$; Right term: $-x^2 -2x +1$. Sum: $(-x^2 -x^2)+(-2x-2x)+(4+1)=-2x^2-4x+5$? Correction: Wait, total tiles: $-2x^2-4x+(4-1)=-2x^2-4x+3$. Option B sum: $(-x²-2x+4)+(-x²-2x-1)=-2x²-4x+3$. Yes, matches.

Answer:

B. $(-x^{2} - 2x + 4) + (-x^{2} - 2x + 1) = -2x^{2} - 4x + 3$