If u = a x + b y + c z ,   v = a y + b z + c x ,   w = a z + b x + c y , then the value of a b c b c a c a b × x y z y z x z x y is

Step-by-step solution

Let a b c b c a c a b × x y z y z x z x y be equal to ∆ . Apply the determinant multiplication formula we get, Δ = a x + b y + c z a y + b z + c x a z + b x + c y b x + c y + a z b y + c z + a x b z + c x + a y c x + a y + b z c y + a z + b x c z + a x + b y Given, u = a x + b y + c z v = a y + b z + c x w = a z + b x + c y Substituting the above values in ∆ , we get, Δ = u v w w u v v w u Expanding the above with respect to R 1 , we get, u u 2 - v w - v u w - v 2 + w ( w 2 - v u ) &#8756