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Answer on Combinatorics | Number Theory Question for Kshitij D Gajapure

Question #15039
Peter picked 4 positive integers a,b,c and d. He wanted to determine the polynomial f(x)= (1−x)^(a+b+c+d)(1+x)^(a+b+c)(1−x+x2)^(a+b)(1+x+x2)^a. He felt lazy and ignored any term that involved x taken to a power larger than 4. He was surprised to see that the result was the term . What is the value of ?
Expert's answer
This question contains mistake in formulation: there is no formulas provided in
last 2 sentences, but they are necessary.

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