Why do commuting operators M₁ and M₂ give that second line?

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Raptor112
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Homework Statement


It is known that ##M_1,M_2, M_3## commute with each other but I don't see how the second line is achieved even though it says that it's using that ##M_1## and ##M_2## commute?
Handwritten derivation of M2|Ψ⟩ as a chain of equalities: M2(1+M1)(1+M2)(1+M3)|000⟩, then (1+M1)(M2+M2²)(1+M3)|000⟩ with the note 'Using commutations of M1 and M2', then (1+M1)(1+M2)(1+M3)|000⟩, ending with |Ψ⟩; a handwritten '1 mark' is in the corner.
 

Discussion

Note M2(1+M1) = M2 + M2M1

How can you rewrite the right hand side using the fact that M1 and M2 commute?
 
TSny said:
Note M2(1+M1) = M2 + M2M1

How can you rewrite the right hand side using the fact that M1 and M2 commute?

##M_2 + M_1M_2##
 
Raptor112 said:
##M_2 + M_1M_2##
OK. Can you see something you can do with this expression that will help?
 
TSny said:
OK. Can you see something you can do with this expression that will help?
##(1 +M_1)M_2## ?
 

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