Simplify :
`(a - 2b + c)^3 - (a - 2b)^3 - 3c ( a - 2b +c)(a - 2b)`

Let's simplify:- a^2(b^2 - c^2) + b^2 (c^2 - a^2) + c^2 (a^2 - b^2)

If b/(a + b) = (3a - c - b)/(2b + c -a) = (-a+3c)/(2a - b + 3c) ( "where " a + b + c ne 0) , then prove that a = b = c .

(a-2b)^(3)+(c-a)^(3)+(2b-c)^(3)

Simplify : (x^(a+b).x^(a-b).x^(c-2a))/(x^(c-a)) .

If 2a = 3b = 4c , then a : b : c will be

(3a-2b)^(3)+(2b-5c)^(3)+(5c-3a)^(3)

To multiply (3a+2b) by (a-b-c).

Simplify root(3)(a^(-2)).b xx root(3)(b^(-2)).c root(3)(c^(-2)).a .

(2a-3b)^(3)+(4c-2a)^(3)+(3b-4c)^(3)

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)