`a)x³+6x²+12x+8`
`=x³+3.x².2+3.x.2²+2³`
`=(x+2)³`
Áp dụng HĐT:`(A+B)³=A³+3A²B+3AB²+B³`
`b)x³-3x²+3x-1`
`=x³-3.x².1+3.x.1²-1³`
`=(x-1)³`
Áp dụng HĐT:`(A-B)³=A³-3A²B+3AB²-B³`
`c)1-9x+27x²-27x³`
`=1-3.1².3x+3.1.(3x)²-(3x)³`
`=(1-3x)³`
Áp dụng HĐT:`(A-B)³=A³-3A²B+3AB²-B³`
`d)x³+3/2x²+3/4x+1/8`
`=x³+3.x². 1/2+3.x. (1/2)^2+(1/2)^3`
`=(x+1/2)^3`
Áp dụng HĐT:`(A+B)³=A³+3A²B+3AB²+B³`
`e)27x³-54x²y+36xy²-8y³`
`=(3x)³-3.(3x)².2y+3.3x.(2y)²-(2y)³`
`=(3x-2y)³`
Áp dụng HĐT:`(A-B)³=A³-3A²B+3AB²-B³`
`f)x²-2xy+y²-4m²+4mn-n²`
`=(x²-2xy+y²)-(4m²-4mn+n²)`
`=(x²-2.x.y+y²)-[(2m)²-2.2m.n+n²]`
`=(x-y)²-(2m-n)²`
`=(x-y+2m-n)(x-y-2m+n)`
Áp dụng HĐT:`(A-B)²=A²-2AB+B²`
`A²-B²=(A+B)(A-B)`
