`#tnvt`
`a)x^2+6xy+9y^2`
`=x^2+2.3y.x+(3y)^2`
`=(x+3y)^2`
`b)10x-25-x^2`
`=-x^2+10x-25`
`=-(x^2-10x+25)`
`=-(x^2-2.5.x+5^2)`
`=-(x-5)^2`
`c)121x^4-y^2`
`=(11x^2)^2-y^2`
`=(11x^2-y)(11x^2+y)`
`d)125x^3-\frac{y^3}{27}`
`=(5x)^3-(y/3)^3`
`=(5x-y/3)(25x^2+(5xy)/3+(y^2)/9)`
`e)27+x^3y^6`
`=3^3+(xy^2)^3`
`=(3+xy^2)(9-3xy^2+x^2y^4)`