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Minimizing the number of terms of the square of a polynomial
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Suppose a, b, c, and d belong to the set of nonzero integers.
Let P(x) = (x^{4 }+ ax^{3} + bx^{2} + cx + d)^{2}.
Determine one of the sets of values of a, b, c, and d, such that when P(x) is
expanded into individual terms of an 8th degree polynomial, that polynomial
will have the fewest number of nonzero terms possible.
Bonus:
Write P(x) in its expanded form.
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