Using properties of determinants prove that:


Expanding with R1


=b2c2(a2c+abc-abc-a2b)-bc(a3c2+a2bc2-a2b2c-a3b2)+(b+c)(a3bc2-a3b2c)


=a2b3c2-a2b3c2-a3bc2-a2b3c2+a2b3c2+a3b3c+a3b2c2-a3b3c+a3bc3-a3b2c2


=0


1