Using properties of determinants prove that: |(a, b, ax + by)(b, c, bx+cy)(ax +by, bx+cy, 0)|

Hi, I have a question and I hope anyone could answer it:

Using properties of determinants prove that:

(begin{vmatrix}
a & b& ax+by \[0.3em] b& c & bx + cy \[0.3em] ax + by &bx +cy & 0
end{vmatrix}) = (b²-ac) (ax² + 3bxy + cy²)