Without expanding the following determinant, show that : `|[3a+b, 2a, a],[4a+3b, 3a, 3a],[5a+6b,4a,6a]|=a^3`

Without expanding the following determinant, show that : |[[3x+y, 2x, x],[4x+3y, 3x, 3x],[5x+6y,4x,6x]]|=x^3

Without expanding the following determinant, show that : |[[3p+q, 2p, p],[4p+3q, 3p, 3p],[5p+6q,4p,6p]]|=p^3

Expand the following (3a-2b)^3

Without expanding show that the following determinants vanish |(42,1,6),(28,7,4),(14,3,2)|

Without expanding show that the following determinants vanish |(4,a,b+c),(4,b,c+a),(4,c,a+b)|

Without expanding show that the following determinants vanish |(3,1,6),(5,2,10),(7,4,14)|

Expand the following (3a-5b-c)^2

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]| = a^3

Write the following cube in the expanded form: (3a + 4b)^3