Question

Answer 1

\(a,\\ =x^2+2x+1+2y^2-12y+18-8\\ =\left(x+1\right)^2+2\left(y-3\right)^2+\left(-8\right)\\ b,\\ =x^2+2xy+y^2+4x^2-4x+1-8\\ =\left(x+y\right)^2+\left(2x-1\right)^2+\left(-8\right)\)

\(c,\\ =x^2-4xy+4y^2+y^2-6y+9-2023\\ =\left(x-2y\right)^2+\left(y-3\right)^2+\left(-2023\right)\\ d,\\ =x^2+x^2+y^2+4y^2-2xy-8x+8y+16+4-10\\ =x^2-8x+16+x^2-2xy+y^2+4y^2+8y+4-10\\ =\left(x-4\right)^2+\left(x-y\right)^2+\left(2y+2\right)^2+\left(-10\right)\)

 

Answer 2

`a,x^2 + 2y^2 + 2x - 12y + 11`.

`= x^2 + 2x + 1 + 2y^2 - 12y + 18 - 8`.

`= (x+1)^2 + 2(y-3)^2 - 8`.

`b, 5x^2 + y^2 + 2xy - 4x -7`

`= (x+y)^2 + (2x-1)^2 - 8`.

`c, x^2 + 4y^2 - 4xy + y^2 - 6y + 9 - 2025.`

`= (x-2y)^2 + (y-3)^2 -2025.`