Lời giải :
`a)`
`2x(x+1)+2(x+1)`
`=(x+1)(2x+2)`
`=2(x+1)(x+1)`
`=2(x+1)^2`
`b)`
`3x.(x+1)^(2)-5x^(2).(x+1)+7.(x+1)`
`=(x+1)[3x(x+1)-5x^(2)+7]`
`=(x+1)(3x^(2)+3x-5x^(2)+7)`
`=(x+1)(-2x^(2)+3x+7)`
`c)`
`4x(x-2y)+8y(2y-x)`
`=4x(x-2y)-8y(x-2y)`
`=(4x-8y)(x-2y)`
`=4(x-2y)(x-2y)`
`=4(x-2y)^2`
`d)`
`x^(2)-6xy+9y^2`
`=x^(2)-2.x.3y+(3y)^2`
`=(x-3y)^2`
`e)`
`(2x-1)^(2)-(x-1)^2`
`=(2x-1-x+1)(2x-1+x-1)`
`=x(3x-2)`
`g)`
`25.(x-y)^(2)-16.(2+y)^2`
`=[5(x-y)]^(2)-[4(2+y)]^2`
`=(5x-5y)^(2)-(8+4y)^2`
`=(5x-5y-8-4y)(5x-5y+8+4y)`
`=(5x-9y-8)(5x-y+8)`