Question

This is a basic question.

since

(ab)^m = a^m b^m

then

(A^2 - B^2) --> (A - B)^2

If that is the case

(A-B)^2 --> (A-B)(A-B) -->

F -----> A^2
O ---->AB
I ----->AB
L ----->B^2

therefore

A^2 - AB -AB -B^2 = A^2 - 2AB -B^2

Yet my book says:

A^3 + B^3 = (A+B)( A^2 -AB+ B^2)

I am having problems factoring cubes. Where is my logic wrong? Thank you, and I apologize for the basic question. I am new to this and appreciate your patience.

Answer 1

I think that instead of I being AB I think it should be BA. Try replacing that

Answer 2

(A^2 - B^2) --> (A - B)^2 is not true
(A^2 - B^2) --> (A - B)(A + B) because it is a difference of squares

Answer 3

and as for factoring cubes...
(A+B)( A^2 -AB+ B^2) =
A(A^2) - A(AB) + A(B^2) + B(A^2) - B(AB) + B(B^2)
A^3 - A^2B + AB^2 + A^2B - AB^2 + B^3
A^3 + 0 + 0 + B^3
A^3 + B^3

Answer 4

I always thought (ab)^m = a^m b^m, raising a product to a power.

You have told me this is not true.
I will continue to research, since this is a basic principle I have come to know.

Thank you.