The value of the determinant `|xx+y x+2y x+2y xx+y x+y x+2y x|i s` `9x^2(x+y)` (b) `9y^2(x+y)` `3y^2(x+y)` (d) `7x^2(x+y)`

Explanation

`r_1 -> r_1- r_3 ; r_2-> r_2 - r_3`

`/_ = |(-y,-y,2y),(y,-2y,y),(x+y, x+2y,x)|`

`= y^2 |(-1,-1,2),(1,-2,1),(x+y, x+2y, x)|`

`r_1 -> r_1 + r_2`

`/_ = y^2 |(0,-3,3),(1,-2,1),(x+y, x+2y, x)|`

`= y^2[ -1(-3x- 3x-6y)+ (x+y)(-3+6)]`

`= y^2[6(x+y) + 3(x+y)]`

`=y^2 *9(x+y)`

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