Big-Exponent Polynomial

Algebra Level 4

Peter picked 4 positive integers \(a, b, c\) and \(d\). He wanted to determine the polynomial \( f(x)=\) \( \small (1\!-\!x)^{a+b+c+d} (1\!+\!x)^{a+b+c}(1\!-\!x\!+\!x^2)^{a+b}(1\!+\!x\!+\!x^2)^a \). He felt lazy and ignored any term that involved \(x\) taken to a power larger than or equal to 3. He was surprised to see that the result was the term \( 1-21x \). What is the value of \(c\)?

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