Question

which sum or difference is modeled by the algebra tiles?
a. $(x^{2}-2x+3)-(-x^{2}-4x-2)=2x-1$
b. $(x^{2}-2x-3)+(x^{2}-4x+2)=2x-1$
c. $(x^{2}-2x-3)-(x^{2}+4x+2)=2x-1$
d. $(x^{2}-2x-3)+(-x^{2}+4x+2)=2x-1$

Explanation:

Step1: Identify total tile values

Blue tiles (positive): $x^2 + 4x + 2$
Red tiles (negative): $-x^2 - 2x - 3$
Total expression: $x^2 + 4x + 2 - x^2 - 2x - 3$

Step2: Simplify like terms

Combine $x^2$ terms: $x^2 - x^2 = 0$
Combine $x$ terms: $4x - 2x = 2x$
Combine constants: $2 - 3 = -1$
Simplified result: $2x - 1$

Step3: Match to option format

Rewrite total expression as sum: $(x^2 - 2x - 3) + (-x^2 + 4x + 2)$

Answer:

D. $(x^2 - 2x - 3) + (-x^2 + 4x + 2) = 2x - 1$