Answer
$b^2(3a+b)$
Work Step by Step
The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$
where $det =\begin{vmatrix}p & q \\r & s\end{vmatrix}$
$det=(a+b)\begin{vmatrix}a+b &a \\a & a+b\end{vmatrix}-a \begin{vmatrix}a & a \\a & a+b\end{vmatrix}+a \begin{vmatrix}a & a \\a+b & a\end{vmatrix}$
or, $=(a+b) [a^2+2ab+b^2-a^2]-a[a^2+ab-a^2] +a [a^2-a^2-ab]$
or, $=2a^2b+ab^2+2ab^2+b^3-2a^2b$
or, $=b^2(3a+b)$
