Let $P(x)=\left(2 x^{2}-2 x+1\right)^{17}\left(3 x^{2}-3 x+1\right)^{17}$. Find

a) the sum of the coefficients of this polynomial;

b) the sums of the coefficients at even and odd powers of $x$.

#
The sum of the coefficients is $P(1)=1$. The sum of the coefficients at even powers is $1 / 2(P(1)+P(-1))=1 / 2$ $\left(1+5^{17} 7^{17}\right)$. Accordingly, the sum of the coefficients at odd powers is $1 / 2(P(1)-P(-1))=1 / 2(1-$ $\left.2^{17} 7^{17}\right)$.

## Answer

a) 1 ; b) $1 / 2\left(1+35^{17}\right), 1 / 2\left(1-35^{17}\right)$.