Final answer:
To evaluate AB and BA, we substitute the given values for A and B and perform the necessary calculations.
Step-by-step explanation:
To evaluate AB, we substitute the given values for A and B:
A = D + 2 and B = 3D - 1
Substituting A in terms of D, we have:
A = (D + 2)
Substituting B in terms of D, we have:
B = 3(D) - 1
Expanding and simplifying, we have:
AB = (D + 2)(3D - 1)
Multiplying these terms, we get:
AB = 3D^2 - D + 6D - 2
Combining like terms, we have:
AB = 3D^2 + 5D - 2
To evaluate BA, we substitute the given values for A and B:
A = D + 2 and B = 3D - 1
Substituting A in terms of D, we have:
A = (D + 2)
Substituting B in terms of D, we have:
B = 3(D) - 1
Expanding and simplifying, we have:
BA = (3D - 1)(D + 2)
Multiplying these terms, we get:
BA = 3D^2 + 5D - 2
Combining like terms, we have:
BA = 3D^2 + 5D - 2