`1.`
`a)x²-xy+x-y`
`=(x²-xy)+(x-y)`
`=x(x-y)+(x-y)`
`=(x-y)(x+1)`
`b)a³-a²x-ay+xy`
`=(a³-a²x)-(ay-xy)`
`=a²(a-x)-y(a-x)`
`=(a-x)(a²-y)`
`c)3x²+12x+12`
`=3(x²+4x+4)`
`=3(x²+2.x.2+2²)`
`=3(x+2)²`
`d)2a²-2b²-5a+5b`
`=(2a²-2b²)-(5a-5b)`
`=2(a²-b²)-5(a-b)`
`=2(a+b)(a-b)-5(a-b)`
`=(a-b)[2(a+b)-5]`
`=(a-b)(2a+2b-5)`
`e)x²y-xy²-3x²+3y²`
`=(x²y-xy²)-(3x²-3y²)`
`=xy(x-y)-3(x²-y²)`
`=xy(x-y)-3(x+y)(x-y)`
`=(x-y)[xy-3(x+y)]`
`=(x-y)(xy-3x-3y)`
`f)x³+5x²-4x-20`
`=(x³+5x²)-(4x+20)`
`=x²(x+5)-4(x+5)`
`=(x+5)(x²-4)`
`=(x+5)(x²-2²)`
`=(x+5)(x+2)(x-2)`
`2.`
`a)x²+6x-7`
`=x²+7x-x-7`
`=(x²+7x)-(x+7)`
`=x(x+7)-(x+7)`
`=(x+7)(x-1)`
`b)3x²+10x+7`
`=3x²+3x+7x+7`
`=(3x²+3x)+(7x+7)`
`=3x(x+1)+7(x+1)`
`=(x+1)(3x+7)`
`c)1/2(x^2+y^2)^2-2x²y²`
`=1/2(x^4+2x²y²+y^4)-2x²y²`
`=1/2x^4+x²y²+1/2y^4-2x²y²`
`=1/2x^4-x²y²+1/2y^4`
`=1/2(x^4-2x²y²+y^4)`
`=1/2[(x^2)^2-2.x².y²+(y^2)^2]`
`=1/2(x²-y²)^2`
`=1/2[(x+y)(x-y)]^2`
`=1/2(x+y)²(x-y)²`
`d)x²(y-z)+y²(z-x)+z²(x-y)`
`=x²y-x²z+y²z-xy²+z²(x-y)`
`=(x²y-xy²)-(x²z-y²z)+z²(x-y)`
`=xy(x-y)-z(x²-y²)+z²(x-y)`
`=xy(x-y)-z(x+y)(x-y)+z²(x-y)`
`=(x-y)[xy-z(x+y)+z²]`
`=(x-y)(xy-xz-yz+z²)`
`=(x-y)[(xy-xz)-(yz-z²)]`
`=(x-y)[x(y-z)-z(y-z)]`
`=(x-y)(y-z)(x-z)`
