`1)4x^2-12x+9`
`=(2x)^2-2.2x.3+3^2`
`=(2x-3)^2`
`2)1+8x^6y^3`
`=(2x^2y)^3+1`
`=(2x^2y+1)(4x^4y^2-2x^2y+1)`
`3)x^3+6x^2+12x+8`
`=x^3+3x^2`.`2+3x.2^2+2^3`
`=(x+2)^3`
`4)x^3-3x^2+3x-1`
`=(x-1)^3`
`5)1-9x+27x^2-27x^3`
`=1-3.1^2`.`3x+3.1.(3x)^2-(3x)^3`
`=(1-3x)^3`
`6)x^3+(3/2)x^2+(3/4)x+1/8`
`=x^3+3x^2`.`1/2+3x(1/2)^2+(1/2)^3`
`=(x+1/2)^3`
`7)27x^3-54x^2y+36xy^2-8y^3`
`=(3x)^3-3.(3x)^2`.`2y+3.3x(2y)^2-(2y)^3`
`=(3x-2y)^3`
`8)x^2-4x^2y^2+y^2+2xy`
`=(x^2+2xy+y^2)-4x^y^2`
`=(x+y)^2-(2xy)^2`
`=(x+y-2xy)(x+y+2xy)`
`9)x^6-y^6`
`=(x^3)^2-(y^3)^2`
`=(x^3-y^3)(x^3+y^3)`
`=(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)`
`10)25-a^2+ab-b^2`
`=25-(a^2-2ab+b^2)`
`=5^2-(a-b)^2`
`=(5-a+b)(5+a-b)`
`11)3x^2+9x-30`
`=3(x^2+3x-10)`
`=3[x^2-2x+5x-10]`
`=3[(x^2-2x)+(5x-10)]`
`=3[x(x-2)+5(x-2)]`
`=3(x-2)(x+5)`
`12)x^2+4xy-21y^2`
`=x^2+7xy-3xy-21y^2`
`=(x^2+7xy)-(3xy+21y^2)`
`=x(x+7y)-3y(x+7y)`
`=(x-3y)(x+7y)`
`13)(x-y)^2+4(x-y)-12`
`=(x-y)^2-2(x-y)+6(x-y)-12`
`=(x-y)(x-y-2)+6(x-y-2)`
`=(x-y+6)(x-y-2)`
`14)x^2-7xy+10y^2`
`=x^2-5xy-2xy+10y^2`
`=(x^2-5xy)-(2xy-10y^2)`
`=x(x-5y)-2y(x-5y)`
`=(x-2y)(x-5y)`
`15)x^2yz+5xyz-14yz`
`=yz(x^2+5x-14)`
`=yz[x^2-7x+2x-14]`
`=yz[(x^2-7x)+(2x-14)]`
`=yz[x(x-7)+2(x-7)]`
`=yz(x+2)(x-7)`
