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Using the property of determinants and w...

Using the property of determinants and without expanding, prove that:`|[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]|`

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Using the property of determinants and without expanding {:[( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) ]:}=2 {:[(a,p,x),( b,q,y),(c,r,z)]:}

Using the property of determinants and without expanding {:|( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) |:}=2 {:|(a,p,x),( b,q,y),(c,r,z)|:}

Using the property of determinants and without expanding {:[( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) ]:}=2 {:[(a,p,x),( b,q,y),(c,r,z)]:}

Using the property of determinants and without expanding {:|( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) |:}=2 {:|(a,q,x),( b,q,y),(c,r,z)|:}

Using the property of determinants and without expanding {:[( x,a,x+a),( y,b,y+b),(z,c,z+c)]:} =0