How does this seemingly-trivial simplification work? In a section on inductive proofs in the book M

Grimanijd 2022-07-03 Answered
How does this seemingly-trivial simplification work?
In a section on inductive proofs in the book Modelling Computing Systems: Mathematics for Computer Science (Muller, Struth) there is a simplification that is assumed to be trivial, but that I can't figure out.
It occurs in this step:
k ( k + 1 ) ( k + 2 ) 3 + ( k + 1 ) ( k + 2 ) = ? ( k + 1 ) ( k + 2 ) ( k + 3 ) 3
How does one get from the first expression to the second?
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Answers (2)

wasipewelr
Answered 2022-07-04 Author has 11 answers
k ( k + 1 ) ( k + 2 ) 3 + ( k + 1 ) ( k + 2 ) = k ( k + 1 ) ( k + 2 ) + 3 ( k + 1 ) ( k + 2 ) 3 = ( k + 1 ) ( k + 2 ) ( k + 3 ) 3
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Riya Hansen
Answered 2022-07-05 Author has 4 answers
Hint:
( k + 1 ) ( k + 2 ) = 3 ( k + 1 ) ( k + 2 ) 3 .
Now combine the fractions and factor out ( k + 1 ) ( k + 2 )
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