" 21.Evaluate "a^(x-y),a^(y-z),a^(z-x),

If (a+b+c)=0, then a^(3)+b^(3)+c^(3)=3abc Find the value of (x-y)^(3)+(y-z)^(3)+(z-x)^(3)

The following steps are involved in finding the value of (a^(x+y))^(x-y)(a^(y+z))^(y-z)(a^(z+x))^(z-x) . Arrange them in sequantial order. (A) a^((x+y)(x-y).a^(y+z)(y-z).a^((z+x)(z-x)) (B) a^0=1 (C) a^(x^2-y^2).a^(y^2-z^2).a^(z^2-x^2) (D) a^(x^2-y^2+y^2-z^2+z^2-x^2)

Use properties of determinants to evaluate : |{:(x+y,y+z,z+x),(z,x,y),(1,1,1):}|

Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y),(1,1,1)|

Using Cofactors of elements of third column, evaluate Delta=|(1,x, y z),(1,y, z x),(1,z, x y)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|

Using coafactors of the elements of third row, evaluate Delta=|{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Let's find value of : (x - y)a + (y - z) b + (z -x)c if a = x^2 + xy + y^2,b = y^2 + yz + z^2, c = z^2 + zx + x^2