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The question is to explain the expression ( 30 + 31 + 32 ) ( 20 + 21 + 22 ) ( 50 + 51 + 52 ) ( 110 +111) i.e. how do we get it , not how to simplify it.
Now,
Let us consider a smaller example .
12 = 22.3
Look at the factors of 12 i.e. 1 , 2 , 3 , 4 , 6, 12 or equivalently 1 , 2 , 3 , 22 , 2.3 , 22.3
Note that if we expand the expression ( 1+ 2 + 22) ( 1 + 3 ) , all these terms are included.
The logic is that we can choose the no. of powers of each prime factor . So if all these powers are included , then we get all the factors. that is what we r doing.
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Moderation Team
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