`d)a^4+a³+a³b+a²b`
`=a³(a+1)+a²b(a+1)`
`=(a+1)(a³+a²b)`
`=a²(a+1)(a+b)`
`e)a³+3a²+4a+12`
`=a²(a+3)+4(a+3)`
`=(a+3)(a²+4)`
`f)a³+4a²+4a+3`
`=a³+a²+3a²+a+3a+3`
`=(a³+a²+a)+(3a²+3a+3)`
`=a(a²+a+1)+3(a²+a+1)`
`=(a+3)(a²+a+1)`
`g)x²y+xy²+x²z+xz²+y²z+yz²+2xyz`
`=x²y+xy²+x²z+xz²+y²z+yz²+xyz+xyz`
`=(x²y+xyz)+(x²z+xz²)+(xy²+y²z)+(xyz+yz²)`
`=xy(x+z)+xz(x+z)+y²(x+z)+yz(x+z)`
`=(x+z)(xy+xz+y²+yz)`
`=(x+z)[x(y+z)+y(y+z)]`
`=(x+y)(y+z)(x+z)`
`h)a²+b²+2a-2b-2ab`
`=(a²-2ab+b²)+(2a-2b)`
`=(a-b)²+2(a-b)`
`=(a-b)(a-b+2)`
`i)4a²-4b²-4a+1`
`=(4a²-4a+1)-4b²`
`=[(2a)²-2.2a.1+1²]-(2b)²`
`=(2a-1)²-(2b)²`
`=(2a-1+2b)(2a-1-2b)`
`k)(a+b+c)³-(a+b-c)³-(a-b+c)³-(-a+b+c)³`
`=(a+b+c)³-(a+b-c)³-(-a+b+c)³-(a-b+c)³`
`=(a+b+c)³-(a+b-c)³-(b+c-a)³-(a-b+c)³(**)`
Đặt `x=a+b-c(1)`
`y=b+c-a(2)`
`z=a-b+c(3)`
Cộng vế theo vế `(1),(2)` và `(3)` ta được:
`x+y+z=a+b-c+b+c-a+a-b+c`
`→x+y+z=(a-a+a)+(b+b-b)+(-c+c+c)`
`→x+y+z=a+b+c(4)`
Thay `(1),(2),(3)` và `(4)` vào `(**)` ta được:
`(x+y+z)³-x³-y³-z³`
`=[(x+y+z)³-x³]-(y³+z³)`
`=(x+y+z-x)[(x+y+z)²+x(x+y+z)+x²]-(y+z)(y²-yz+z²)`
`=(y+z){[(x+y)+z]²+x²+xy+xz+x²}-(y+z)(y²-yz+z²)`
`=(y+z){[(x+y)+z]²+x²+xy+xz+x²-(y²-yz+z²)}`
`=(y+z)[(x+y)²+2z(x+y)+z²+x²+xy+xz+x²-y²+yz-z²]`
`=(y+z)(x²+2xy+y²+2xz+2yz+z²+x²+xy+xz+x²-y²+yz-z²)`
`=(y+z)[(x²+x²+x²)+(y²-y²)+(z²-z²)+(2xy+xy)+(2yz+yz)+(2xz+xz)]`
`=(y+z)(3x²+3xy+3yz+3xz)`
`=3(y+z)(x²+xy+yz+xz)`
`=3(y+z)[x(x+y)+z(x+y)]`
`=3(x+y)(y+z)(x+z)`
`=3(a+b-c+b+c-a)(b+c-a+a-b+c)(a+b-c+a-b+c)`
`=3.2b.2c.2a`
`=24abc`
