Given: AB=B and BA=A
lets break the question as :
(A+B)5 = (A+B)2 * (A+B)2 * (A+B)
=(A2+B2+AB+BA)(A2+B2+AB+BA)(A+B)...........@1
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(Since (A+B)2= (A2+AB+BA+B2) = (A*A + AB+BA+B*A)
=(A*BA+AB+BA+B*AB) = ((A*B)A+AB+BA+(B*A)B)
=(BA+AB+BA+AB) = 2(A+B)...............@2
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Puting value of equation @2 in @1 we get :->
=2(A+B)*2(A+B)*(A+B) = 4(A+B)2*(A+B) = 8(A+B)(A+B)
=16(A+B) answer