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Question

Find the number of dissimilar terms in the expansion of (a3+b3+3ab(a+b))50


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Solution

We will first simplify the terms in the bracket so that we can apply binomial expansion.
We know (a3+b3+3ab(a+b)) = (a+b)3. Therefore, we can
write (a3+b3+3ab(a+b))50 as ((a+b)3)50.

It is equal to (a+b)150. There will be a total of (n+1) terms in the expansion of (a+b)n. Therefore the total number terms in the expansion of (a+b)150 is 151


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