$1, ax^2+bx^2+2xy(a+b)+ay^2-by^2$
$= (a - b)(x^2m - 2xy + y^2)$
$2, ax^+bx^2+2xy(a+b)+2ay^2+by^2$
$ =x^2(a+b)+2xy(a+b)+y^2(a+b)$
$ =(x^2+2xy+y^2)(a+b)$
$ =(x+y)^2(a+b)$
$3,x²(a + b) - 4ax - 4bx + 4a + 4b$
$= x²(a + b) - 4x(a + b) + 4(a + b)$
$= (x² - 4x + 4)(a + b)$
$= (x - 2)²(a + b)$
4, \(ax^2+bx^2-6ax+6bx+9a+9b\)
\(=\left(ax^2-6ax+9a\right)+\left(bx^2+6bx+9b\right)\)
\(=a\left(x^2-6x+9\right)+b\left(x^2+6x+9\right)\)
\(=a\left(x-3\right)^2+b\left(x+3\right)^2\)