`#Sad`
`1)`
`5x^2+10x+5-5y^2`
`= 5(x^2+2x+1-y^2)`
`= 5[(x^2+2x+1)-y^2]`
`= 5[(x+1)^2-y^2]`
`= 5(x-y+1)(x+y+1)`
`2)`
`3x^3+6x^2+3x-12xy^3`
`= 3x(x^2+2x+1-4y^2)`
`= 3x[(x^2+2x+1)-(2y)^2]`
`= 3x[(x+1)^2-(2y)^2]`
`= 3x(x-2x+1)(x+2y+1)`
`3)`
`a^3b-ab^2+a^2+2ab+b^2`
`= (a^3b-ab^3)+(a^2+2ab+b^2)`
`= ab(a^2-b^2)+(a+b)^2`
`= ab(a-b)(a+b)+(a+b)^2`
`= (a+b)[ab(a-b)+a+b]`
`= (a+b)(a^2b-ab^2+a+b)`
`4)`
`2x^3-2xy^2-8x^2+8xy`
`= (2x^3-2xy^2)-(8x^2-8xy)`
`= 2x(x^2-y^2)-8x(x-y)`
`= 2x(x-y)(x+y)-8x(x-y)`
`= (x-y)[2x(x+y)-8x]`
`= (x-y)(2x^2+2xy-8x)`
