# 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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