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Bài `1:`
`a)`
`x^4-x^5`
`=x^4*1-x^4*x`
`=x^4(1-x)`
`b)`
`-8x^3y-16x^2y-4xy^2`
`=(-4xy)*2x^2+(-4xy)*4x+(-4xy)*y`
`=-4xy(2x^2+4x+y)`
`c)`
`(x-y)^3-x^3+y^3`
`=(x-y)^3-(x^3-y^3)`
`=(x-y)^3-(x-y)(x^2+xy+y^2)`
`=(x-y)[(x-y)^2-(x^2+xy+y^2)]`
`=(x-y)(x^2-2xy+y^2-x^2-xy-y^2)`
`=-3xy(x-y)`
`d)`
`5x(x-y)^2-(y-x)`
`=5x(x-y)^2+(x-y)`
`=(x-y)[5x(x-y)+1]`
`=(x-y)(5x^2-5xy+1)`
`e)`
`3x(y-x)^3-(x-y)^2`
`=3x(y-x)^3-(y-x)^2`
`=(y-x)^2[3x(y-x)-1]`
`=(y-x)^2(3xy-3x^2-1)`
`g)`
`4x^2-12xy+9y^2`
`=(2x)^2-2*2x*3y+(3y)^2`
`=(2x-3y)^2`
`h)`
`a^4-2a^2+1`
`=(a^2)^2-2*a^2*1+1^2`
`=(a^2-1)^2`
`=[(a-1)(a+1)]^2`
`=(a-1)^2(a+1)^2`
`i)`
`x^3+8`
`=x^3+2^3`
`=(x+2)(x^2-x*2+2^2)`
`=(x+2)(x^2-2x+4)`
`k)`
`x^6-6x^4+12x^2-8`
`=(x^2)^3-3*(x^2)^2*2+3*x^2*2^2-2^3`
`=(x^2-2)^3`
`l)`
`x^3-y^6`
`=x^3-(y^2)^3`
`=(x-y^2)[x^2+x*y^2+(y^2)^2]`
`=(x-y^2)(x^2+xy^2+y^4)`
Bài `2:`
`a)`
`x^2-5=0`
`<=>x^2=5`
`<=>[(x=sqrt5),(x=-sqrt5):}`
Vậy `x\in{sqrt5;-sqrt5}`
`b)`
`x^2-36=0`
`<=>x^2=36`
`<=>[(x=sqrt36),(x=-sqrt36):}`
`<=>[(x=6),(x=-6):}`
Vậy `x\in{6;-6}`
`c)`
`(3x-5)^2-(x+1)^2=0`
`<=>(3x-5-x-1)(3x-5+x+1)=0`
`<=>(2x-6)(4x-4)=0`
`<=>(x-3)(x-1)=0`
`<=>[(x-3=0),(x-1=0):}`
`<=>[(x=3),(x=1):}`
Vậy `x\in{3;1}`
`d)`
`(5x-4)^2-49x^2=0`
`<=>(5x-4)^2-(7x)^2=0
`<=>(5x-4-7x)(5x-4+7x)=0`
`<=>(-2x-4)(12x-4)=0`
`<=>(x+2)(3x-1)=0`
`<=>[(x+2=0),(3x-1=0):}`
`<=>[(x=-2),(x=1/3):}`
Vậy `x\in{-2;1/3}`
`e)`
`4x^4-36x=0`
`<=>4x(x^3-9)=0`
`<=>[(4x=0),(x^3-9=0):}`
`<=>[(x=0),(x^3=9):}`
`<=>[(x=0),(x=root3 9):}`
Vậy `x\in{0;root3 9}`
`#td`
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