$\text{Đáp án+Giải thích các bước giải:}$
`a) (x+1)(x+3)(x+5)(x+7)-9`
`= (x²+8x+7)(x²+8x+15)-9`
`= (x²+8x)²-16-9=(x²+8x)²-25`
`= (x²+8x-5)(x²+8x+5)`
`b) (x²+x)²+4x²+4x+3`
`= (x²+x)²+4(x²+x)+3`
Đặt `x²+x=t ⇒ t²+4t+3=(t+1)(t+3)`
`= (x²+x+1)(x²+x+3)`
`c) (x²+4x+8)²+3x(x²+4x+8)+2x²`
Đặt `x²+4x+8=a`
`⇒ a²+3ax+2x²=a²+ax+2ax+2x²`
`= (a+x)(a+2x)=(x²+5x+8)(x²+6x+8)`
`= (x²+5x+8)(x+2)(x+4)`
`d) (x²+4x+3)(x²+5x+6)-15`
`= (x+1)(x+3)(x+2)(x+3)-15`
`e) x²-2x+y²-2y+2xy+1`
`= (x²+2xy+y²)-2(x+y)+1`
`= (x+y)²-2(x+y)+1`
`=(x+y-1)²`
