Đáp án+Giải thích các bước giải:
Bài `5:`
`a) x³+6x²+12x+8=x³+3.2.x²+3.2².x+2³`
`=(x+2)³`
`b) x³-3x²+3x-1=(x-1)³`
`c) 1-9x+27x²-27x³=(1-3x)³`
`d) x³+(3x²)/2+(3x)/4+1/8=(x+1/2)³`
`e) 27x³-54x²y+36xy²-8y³=(3x-2y)³`
`f) x²-2xy+y²-4m²+4mn-n²`
`=(x-y)²-(2m-n)²`
`=(x-y-2m+n)(x-y+2m-n)`
*Áp dụng HĐT: `(a-b)³=a³-3a²b+3ab²-b³`
`(a+b)³=a³+3a²b+3ab²+b³`
Bài `6:`
`a) x²-4x²y²+y²+2xy=(x+y)²-(2xy)²`
`=(x+y-2xy)(x+y+2xy)`
`b) x^6-y^6=(x³-y³)(x³+y³)`
`=(x-y)(x²+xy+y²)(x+y)(x²-xy+y²)`
`c) 25-x²+2xy-y²=5²-(x-y)²`
`=(5-x+y)(5+x-y)`
`d) 4b²c²-(b²+c²-a²)²`
`=(2bc)²-(b²+c²-a²)²`
`=(2bc-b²-c²+a²)(2bc+b²+c²-a²)`
`=[a²-(b²-2bc+c²)][(b²+2bc+c²)-a²]`
`=[a²-(b-c)²][(b+c)²-a²]`
`=(a-b+c)(a+b-c)(b+c-a)(b+c+a)`
`e) (x+y+z)²+(x+y-z)²-4z²`
`=(x+y+z)²+(x+y+3z)(x+y-5z)`
`f) 9(x+y-1)²-4(2x+3y+1)²`
`=[3(x+y-1)]²-[2(2x+3y+1)]²`
`=(3x+3y-3)²-(4x+6y+2)²`
`=(3x+3y-3-4x-6y-2)(3x+3y-3+4x+6y+2)`
`=-(x+3y+5)(7x+9y-1)`
