Prove: `|(a, a+b, a+2b),( a+2b, a ,a+b ),(a+b, a+2b, a)|=9(a+b)b^2`

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Without expanding, prove the following |(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a)|=9(a+b)b^2

Without expanding the determinants,show that |(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a)|=9(a+b)b^2

Using properties of determinant show that : |(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a)|=9b^2(a+b)

Using properties of determinats show that |{:(a,a+b,a+2b),(a+2b,a,a+b),(a+b,a+2b,a):}|=9b^2(a+b)

Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b^2c^2

Prove that: |(-2a , a+b, a+c),( b+a,-2b, b+c),( c+a , c+b,-2c)|=4(a+b)(b+c)(c+a)

Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

Prove that: |(-2a , a+b , a+c ) ( b+a ,-2b , b+c ) ( c+a, c+b , -2c)| =4(a+b)(b+c)(c+a)

Prove: |[a+b+2c, a, b], [c, b+c+2a, b], [c ,a ,c+a+2b]|=2(a+b+c)^3