a)x^3-2x^2y+xy^2-9x b) (x+y)^2-(x-y)^2 c) (3x+1)^2-(x+1)^2 d) 25^2-15^2 e) x^2-x-y^2-y h) x^2-2xy+y^2-z^2 g) 5x-5y+ax-ay m) a^3-a^3x-ay+xy

`a)x³-2x²y+xy²-9x`

`=x(x²-2xy+y²-9)`

`=x[(x²-2xy+y²)-9]`

`=x[(x-y)²-3²]`

`=x(x-y+3)(x-y-3)`

`b)(x+y)²-(x-y)²`

`=(x+y+x-y)(x+y-x+y)`

`=2x.2y`

`=4xy`

`c)(3x+1)²-(x+1)²`

`=(3x+1+x+1)(3x+1-x-1)`

`=2x(4x+2)`

`=4x(2x+1)`

`d)25²-15²`

`=(25+15)(25-15)`

`=40.10`

`=400`

`e)x²-x-y²-y`

`=(x²-y²)-(x+y)`

`=(x+y)(x-y)-(x+y)`

`=(x+y)(x-y-1)`

`h)x²-2xy+y²-z²`

`=(x²-2xy+y²)-z²`

`=(x-y)²-z²`

`=(x-y+z)(x-y-z)`

`g)5x-5y+ax-ay`

`=(5x-5y)+(ax-ay)`

`=5(x-y)+a(x-y)`

`=(x-y)(5+a)`