`11)`
`x^2 + xy - 2x - 2y`
` = x (x+y) - 2(x+y)`
` = (x-2)(x+y)`
`12)`
`x^2 (x^2-6) - x^2 + 9`
` = x^4 - 6x^2 - x^2 + 9`
`= x^4 - 7x^2 + 9`
`= (x^4 + x^3 - 3x^2) - (x^3 + x^2 - 3x) - (3x^2 + 3x -9)`
`= x^2 (x^2 + x - 3) - x (x^2 + x - 3) - 3 (x^2 + x - 3)`
` = (x^2 - x - 3)(x^2 + x - 3)`
`13)`
`y^2 - 3xy + 6y - 18x`
` = (y^2 + 6y) - (3xy + 18x)`
` = y (y+6) - 3x (y+6)`
`= (y-3x)(y+6)`
`14)`
`3x (x-y) + 6(y-x)`
`= 3x (x-y) - 6(x-y)`
` = (3x-6)(x-y)`
` = 3(x-2)(x-y)`
`15)`
`9 (x-2)^2 - (y+3)^2`
`= [ 3(x-2)]^2 - (y+3)^2`
` = (3x - 6)^2 - (y+3)^2`
`= [ (3x-6) - (y+3)] . [ (3x-6) + (y+3)]`
` = (3x - 6 - y - 3)(3x-6+y+3)`
` = (3x - y - 9)(3x +y - 3)`
`16)`
`x^6 - x^4 - 9x^3 + 9x^2`
` = x^4 (x^2 - 1) - 9x^2 (x-1)`
` = x^4 (x+1)(x-1) - 9x^2 (x-1)`
` = (x-1) [ x^4 (x+1) - 9x^2]`
` = (x-1) (x^5 + x^4 - 9x^2)`
` = (x-1) . x^2 . (x^3 + x^2 - 9)`
`17)`
`x (y^2-1) + 5 (1-y^2)`
` = x(y^2- 1) - 5 (y^2-1)`
` = (x-5)(y^2 - 1)`
` = (x-5)(y-1)(y+1)`
`18)`
`x^2 - 4y^2 + 16x + 64`
` = (x^2 + 16x + 64) - 4y^2`
` = (x^2 + 2 . x . 8 + 8^2) - (2y)^2`
` = (x+8)^2 - (2y)^2`
` = (x+8-2y)(x+8+2y)`
`19)`
`xy^2 + 2y^2 + 2xy + 4y`
` = y^2 (x+2) + 2y (x+2)`
` = (y^2 + 2y)(x+2)`
` = y (y+2)(x+2)`
`20)`
`10x (x-y) - 6y(y-x)`
` = 10x (x-y) + 6y(x-y)`
` = (10x + 6y)(x-y)`
` = 2 (5x + 3y)(x-y)`
`21)`
`25(x+5)^2 - 9 (x+7)^2`
` = [ 5 (x+5)]^2 - [ 3 (x+7)]^2`
` = (5x + 25)^2 - (3x + 21)^2`
`= [ (5x+25) + (3x+21)] . [ (5x+25) - (3x+21)]`
` = (5x + 25 + 3x + 21)(5x+ 25 - 3x- 21)`
` = (8x + 46)(2x + 4)`
` = 2 (4x + 23) . 2 (x+2)`
` = 4 (4x+23)(x+2)`
