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Without expanding, prove that |(a+b x,...

Without expanding, prove that `|(a+b x, c+dx, p+q x), (a x+b, c x+d, p x+q),( u, v, w)|=(1-x^2)|(a, c, p),( b, d, q),( u, v, w)|` .

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`Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|=(1-x^2)|[a, c, p],[ b, d, q],[ u, c, w]|`
Solving `LHS`
`Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|`
Applying `R_1->R_1-xR_2`
...
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