Using the properties of determinants, prove that following `|(a-b,-c^2,a^2),(a^2,-c,-a^2),(b^2,c^2,-a-b)|=(a+b+c)^3`

Using the properties of determinants,prove that ollowing det[[a-b,-c^(2),a^(2)a^(2),-c,-a^(2)b^(2),c^(2),-a-b]]=(a+b+c)^(3)

15.Using properties of determinants,prove the following b+c+aa+b

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

Using properties of determinants, prove the following |(3a,-a+b,-a+c),(a-b,3b,c-a),(a-c,b-c,3c)|=3(a+b+c)(ab+bc+ca)

Using properties of determinants, prove that: |[b^2+c^2,a^2,a^2],[b^2,c^2+a^2,b^2],[c^2,c^2,a^2+b^2]|=4a^2b^2c^2

Using properties of determinants, prove that |{:(0, ab^(2), ac^(2)),(a^(2)b, 0, bc^(2)),(a^(2)c, cb^(2), 0):}|=2a^(3)b^(3)c^(3)

Using properties of determinants,prove that det[[-a^(2),ab,acba,-b^(2),bcca,cb,-c^(2)]]=4a^(2)b^(2)c^(2)

Using properties of determinants,prove the following : det[[a,a^(2),bcb,b^(2),cac,c^(2),ab]]=(a-b)(b-c)(c-a)(bc+ca+ab)

Using properties of determinants, show the following: |[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3

Using properties of determinants Prove that |{:(a+b+c,,-c,,-b),(-c,,a+b+c,,-a),( -b,,-a,,a+b+c):}| = 2 (a+b) (b+c) (c+a)