Question

证明行列式a^2 (a+1)^2 (a+2)^2 (a+3)^2b^2 (b+1)^2 (b+2)^2 (b+3)^2c

Answer 1

a^2 (a+1)^2 (a+2)^2 (a+3)^2

b^2 (b+1)^2 (b+2)^2 (b+3)^2

c^2 (c+1)^2 (c+2)^2 (c+3)^2

d^2 (d+1)^2 (d+2)^2 (d+3)^2 =

a^2 2a+1 4a+4 6a+9

b^2 2b+1 4b+4 6b+9

c^2 2c+1 4c+4 6c+9

d^2 2d+1 4d+4 6d+9 =

a^2 2a+1 2 6

b^2 2b+1 2 6

c^2 2c+1 2 6

d^2 2d+1 2 6 =

a^2 2a+1 2 0

b^2 2b+1 2 0

c^2 2c+1 2 0

d^2 2d+1 2 0 = 0