Distributive Law in Boolean Algebra problem

Question

Im practicing boolean algebra on the following problem

(A+B)(¬A+¬B)

In my textbook they apply the distributive property to get

A(¬A+¬B)+B(¬A+¬B) 

Im not quite sure how this is being applied and would appreciate some clarification.

I know the distributive property is defined as followed

A(B+C)=(AB)+(AC)

But in our problem we have (A+B)(¬A+¬B) not (AB)+(AC)

Answer 1

I know the distributive property is defined as followed

A(B+C)=(AB)+(AC)

It is also the case that conjunction is commutative, so

 (A+B)(¬A+¬B) = (¬A+¬B)(A+B)          Commute
              = (¬A+¬B)A+(¬A+¬B)B     Distribute
              = A(¬A+¬B)+B(¬A+¬B)     Commute

Answer 2

They implicitly assumed $C=A'+B'$, and so $$(A+B)(A'+B')=(A+B)C$$$$=AC+BC=A(A'+B')+B(A'+B')$$ Hope this helps. Ask anything if not clear :)