Prove, using properties of determinants: `|[y+k, y, y],[ y, y+k, y],[ y, y, y+k]|=k^2(3y+k)`

By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k)

Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

Using the properties of determinats, show that |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^(2)(3y+k)

Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

show that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^(2)(3y+k)

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

By using properties of determinants , show that : (i) {:[( x+4, 2x, 2x),( 2x,x+4, 2x),( 2x,2x, x+4) ]:}=( 5x +4) (4-x)^(2) ( ii) {:[( y+k , y , y ),( y,y+ k , y ),( y,y , y+k ) ]:} =k^(2) ( 3y +k )

By using properties of determinants , show that : (i) {:|( x+4, 2x, 2x),( 2x,x+4, 2x),( 2x,2x, x+4) |:}=( 5x +4) (4-x)^(2) ( ii) {:|( y+k , y , y ),( y,y+ k , y ),( y,y , y+k ) |:} =k^(2) ( 3y +k )