`1)`
`x^4 +2x^2+1`
`=(x^2)^2 +2.x^2 .1+1^2`
`=(x^2 +1)^2`
`2)`
`4x^2 -12xy+9y^2`
`=(2x)^2 - 2.2x.3y + (3y)^2`
`=(2x-3y)^2`
`3)`
`-x^2 -2xy-y^2`
`=-(x^2 +2xy+y^2)`
`=-(x+y)^2`
`4)`
`(x+y)^2 -2(x+y)+1`
`=(x+y)^2 -2(x+y).1+1^2`
`=(x+y-1)^2`
`5)`
`x^3 -3x^2 +3x-1`
`=x^3 -3.x^2 .1+3.x.1^2 -1^3`
`=(x-1)^3`
`6)`
`x^3 +6x^2 +12x+8`
`=x^3 +3.x^2 .2 +3.x.2^2 +2^3`
`=(x+2)^3`
`7)`
`x^3 +1-x^2 -x`
`=(x+1)(x^2 -x+1)-x(x+1)`
`=(x+1)(x^2 -x+1-x)`
`=(x+1)(x^2 -2x+1)`
`=(x+1)(x-1)^2`
`8)`
`(x+y)^3 -x^3 -y^3`
`=x^3 +3x^2 y+3xy^2 +y^3 -x^3 -y^3`
`=3x^2 y+3xy^2`
`=3xy(x+y)`.
`1)x^4+2x^2+1`
`=(x^2)^2+2*x^2*1+1^2`
`=(x^2+1)^2`
`2)4x^2-12xy+9y^2`
`=(2x)^2-2*2x*3y+(3y)^2`
`=(2x-3y)^2`
`3)-x^2-2xy-y^2`
`=-(x^2+2xy+y^2)`
`=-(x+y)^2`
`4)(x+y)^2-2(x+y)+1`
`=(x+y)^2-2(x+y)*1+1^2`
`=(x+y-1)^2`
`5)x^3-3x^2+3x-1`
`=x^3-3*x^2*1+3*x*1^2-1^3`
`=(x-1)^3`
`6)x^3+6x^2+12x+8`
`=x^3+3*x^2*2+3*x*2^2+2^3`
`=(x+2)^3`
`7)x^3+1-x^2-x`
`=(x+1)(x^2-x+1)-x(x+1)`
`=(x+1)(x^2-x+1-x)`
`=(x+1)(x-1)^2`
`8)(x+y)^3-x^3-y^3`
`=x^3+3x^2y+3xy^2+y^3-x^3-y^3`
`=3x^2y+3xy^2`
`=3xy(x+y)`