`e)`
`-x^2 + 5x + 2xy - 5y - y^2`
` = - (x^2- 2xy + y^2) + (5x-5y)`
`= - (x-y)^2 + 5 (x-y)`
`= [-(x-y) + 5] (x-y)`
`= (y-x+5)(x-y)`
`f)`
`y^2 (x^2+y) - zx^2 - zy`
`= y^2 (x^2 + y) - z (x^2 + y)`
`= (y^2 - z)(x^2 + y)`
`g)`
`x^2 + 4x-12`
`= x^2 - 2x + 6x - 12`
` = x (x-2) + 6 (x-2)`
` = (x-2)(x+6)`
`h) -5x + x^2 -14`
` = x^2 - 7x + 2x -14`
` = x (x-7) + 2 (x-7)`
`= (x-7)(x+2)`
`i)`
`x^3 + 8 + 6x (x+2)`
`= x^3 + 8 + 6x^2 + 12x`
` = x^3+ 3 . x^2 . 2 + 3 . x . 2^2 + 2^3`
` = (x+2)^3`
`j)`
`15x^2 - 7xy - 2y^2`
`= (15x^2 - 10xy) + (3xy - 2y^2)`
`= 5x (3x-2y) + y(3x-2y)`
` = (5x+y)(3x-2y)`
`k)`
`(x^2+6x+5)(x^2+10x+21) + 15`
` = (x^2+ x + 5x+5)(x^2 + 3x + 7x+21) + 15`
`= [ x (x+1) + 5(x+1)] [ x (x+3) + 7 (x+3)] + 15`
`= (x+1)(x+5)(x+7)(x+3) + 15`
`= [ (x+1)(x+7)] [ (x+5)(x+3)] +15`
`= (x^2+ 7x+x+7)(x^2+3x+5x+15) +15`
` = (x^2+8x+7)(x^2 + 8x+15) +15`
` = [ (x^2 + 8x + 11) - 4] [ (x^2 + 8x + 11) + 4] + 15`
` = (x^2 + 8x+11)^2- 4^2 + 15`
`= (x^2-8x+11)^2 - 16+15`
` =(x^2-8x+11)^2-1`
`= (x^2-8x+11-1)(x^2-8x+11+1)`
`= (x^2-8x+10)(x^2-8x+12)`
` = (x^2-8x+10)(x^2- 2x - 6x + 12)`
` = (x^2-8x+10)[ x (x-2) - 6 (x-2)]`
` = (x^2-8x+10)(x-2)(x-6)`
