[" Using properties of determinants prove that "],[[[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,v,w]]]

Prove that /_\ |[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,v,w]]

Prove that triangle = |[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,v,w]|

Delta=[[a+bx,c+dx,p+qxax+b,cx+d,px+qu,v,w]]=(1-x^(2))det[[a,c,pb,d,qu,c,w]]

Prove that Delta=|[a+b x, c+d x, 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]| .

Prove that |(a+bx ,c+dx,p+qx),(ax + b, cx +d, px +q),(u,v,w)|= (1- x^3) |(a,c,p),(b,d,q),(u,v,w)|

Prove that 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,v,w)]:}

Prove that 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,v,w)]:}

Prove that 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,v,w)|:}

Without expanding prove that , |{:(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,v,w):}|

Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(ax^2+b,cx^2+d,px^2+q),(u,v,w)|=(x^4-1){:|(b,d,q),(a,c,p),(u,v,w)|