What is the coefficient of $x$ in the expansion of the determinant$\begin{vmatrix}
(1+x)^2 & (1+x)^4 & (1+x)^6 \\
(1+x)^3 & (1+x)^6 & (1+x)^9 \\
(1+x)^4 & (1+x)^8 & (1+x)^{12} \\
\end{vmatrix}$.
I simplified the determinant to be $x^3(1+x)^{16}(x+2)$,how will i find coefficient of $x$?Someone help me in getting answer?
$x^3(x+2)(x+1)^{16} = x^4(x+1)^{16}+2x^3(x+1)^{16}= a_1x^3+a_2x^4+\cdots + a_{20}x^{20}$. It appears that the term $bx$ does not exist, as suggested by @BolzWeir so we can take $b = 0$.