# But I Can't Expand So Many Terms!

Discrete Mathematics Level 3

Consider the polynomial $$\displaystyle P\left( x \right) =\Large{\prod _{ k=0 }^{ 10 }{ ({ x }^{ { 2 }^{ k } }+{ 2 }^{ k })} }$$

The coefficient of $${ x }^{ 2016 }$$ is equal to $${ 2 }^{ m }$$. What is the value of $$m$$?

Bonus: For $$\displaystyle P(x)=\prod _{ k=0 }^{ n }{ ({ x }^{ { 2 }^{ k } }+{ 2 }^{ k }) }$$, generalize the coefficient of $${ x }^{ q }$$, with $$0\le q\le { 2 }^{ n+1 }-1$$.

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