Lời giải:
Bài `2` :
`a)`
`16(4x+5)^(2)-25(2x+2)^2`
`=[4.(4x+5)]^(2)-[5.(2x+2)]^2`
`=(16x+20)^(2)-(10x+10)^2`
`=(16x+20-10x-10)(16x+20+10x+10)`
`=(6x+10)(26x+30)`
`=2.(3x+5)2.(13x+15)`
`=4(3x+5)(13x+15)`
`b)`
`(x-y+4)^(2)-(2x+3y-1)^2`
`=(x-y+4-2x-3y+1)(x-y+4+2x+3y-1)`
`=(-x-4y+5)(3x+2y+3)`
`c)`
`(x+1)^(4)-(x-1)^4`
`=[(x+1)^2]^(2)-[(x-1)^2]^2`
`=[(x+1)^(2)-(x-1)^2][(x+1)^(2)+(x-1)^2]`
`=(x^(2)+2x+1-x^(2)+2x-1)(x^(2)+2x+1+x^(2)-2x+1)`
`=4x.(2x^(2)+2)`
`=4x.2.(x^(2)+1)`
`=8x(x^(2)+1)`
`d)`
`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)`
Bài `3` :
`a)`
`(x+y)^(2)+8(x+y)+16`
`=(x+y)^(2)+2.(x+y).4+4^2`
`=(x+y+4)^2`
`b)`
`(3x-4)^(2)+2.(3x-4)(5-x)+(x-5)^2`
`=(3x-4)^(2)+2.(3x-4)(5-x)+(5-x)^2`
`=(3x-4+5-x)^2`
`=(2x+1)^2`
