Factorise the following `|(3, a+b+c, a^3+b^3+c^3), (a+b+c, a^2+b^2+c^2, a^4+b^4+c^4), (a^2+b^2+c^2, a^3+b^3+c^3, a^5+b^5+c^5 )|`

Prove that |{:(" "3,a+b+c,a^2+b^2+c^2),(a+b+c,a^2+b^2+c^2,a^3+b^3+c^3),(a^2+b^2+c^2,a^3+b^3+c^3,a^4+b^4+c^4):}|=|{:(1,1,1),(a,b,c),(a^2,b^2,c^2):}|^2

Find the LCM of 14a^2b^3c^4, 20ab^3c^3 and a^5b^4 .

If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :

If a+b+c=0 then prove the following. a^(5)+b^(5) +c^(5)= -5abc (bc+ca +ab) =(5)/(2) abc (a^(2)+b^(2)+c^(2)) =(5)/(6) (a^(2)+b^(2)+c^(2)) (a^(3) +b^(3) +c^(3))

Add: 6a + 8b - 5c, 2b + c - 4a and a - 3b - 2c.

If a : b = 2 : 3 , b: c = 2 : 4, then a : b : c = ?

If a: b is 3: 4 and b: c is 2: 5. Find a: b: c.