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Dear Aditya
Your quetion is not clear in the sense axa can be written as x*a^2. Such type of quetions can be solved by applying row operations i.e. R3 =R3-R2 and R2=R2-R1. Then it will be quite easy to solve the determinant.
All the best.
AKASH GOYAL
AskiitiansExpert-IITD
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|1 a a^2|
|1 b b^2|
|1 c c^2|
= 0 a-b a^2 - b^2 here i am not usin paranthesis it is impossible for me to use so i left it.but you should use
0 b-c b^2 - c^2 R1=R1- R2 R2=R2 - R3 BY DOING SO VALUE OF DET DOESN'T CHANGE
1 c c^2
= (a-b)(b-c) * 0 1 a+b take (a-b) from R1 ;(b-c) from R2
0 1 b+c
= (a-b)(b-c) *{1(b+c)-(a+b)} expand det along C1
= (a-b)(b-c)(c-a)
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