Question

which of the following best describes the difference in the results for the special products ((a + b)^2) and ((a - b)^2)?
choose the correct answer.
a. ((a - b)^2) results in a binomial
b. the signs of each term are positive for ((a + b)^2) and negative for ((a - b)^2)
c. the sign of the middle term is positive for ((a + b)^2) and negative for ((a - b)^2)
d. the last term is positive for ((a + b)^2)

Explanation:

Step1: Expand $(A+B)^2$

$(A+B)^2 = A^2 + 2AB + B^2$

Step2: Expand $(A-B)^2$

$(A-B)^2 = A^2 - 2AB + B^2$

Step3: Compare the two expansions

Analyze signs of each term in both results.

Answer:

C. The sign of the middle term is positive for $(A + B)^2$ and negative for $(A - B)^2$.