Đáp án + Giải thích các bước giải:
`a)` `9x^6+24x^3y^2+16y^4`
`=(3x^3)^2+2*3x^3*4y^2+(4y^2)^2`
`=(3x^3+4y^2)^2`
`b)` `10x^3y^4-25x^6-y^8`
`=-25x^6+10x^3y^4-y^8`
`=-(25x^6-10x^3y^4+y^8)`
`=-[(5x^3)^2-2*5x^3*y^4+(y^4)^2]`
`=-(5x^3-y^4)^2`
`c)` `x^4y^4-z^4`
`=(x^2y^2)^2-(z^2)^2`
`=(x^2y^2-z^2)(x^2y^2+z^2)`
`d)` `x^4+4-4x^2`
`=x^4-4x^2+4`
`=(x^2)^2-2*x^2*2+2^2`
`=(x^2-2)^2`
`l)` `(x^2-2x+1)^3+y^6`
`=(x^2-2x+1)^3+(y^2)^3`
`=(x^2-2x+1+y^2)[(x^2-2x+1)^2-(x^2-2x+1)*y^2+(y^2)^2]`
`=(x^2-2x+1+y^2)[(x^2-2x+1)(x^2-2x+1)-x^2y^2+2xy^2-y^2+y^4]`
`=(x^2-2x+1+y^2)(x^4-4x^3+6x^2-4x+1-x^2y^2+2xy^2-y^2+y^4)`
`e)` `(3x-2y)^2-(2x-3y)^2`
`=[(3x-2y)-(2x-3y)][(3x-2y)+(2x-3y)]`
`=(3x-2y-2x+3y)(3x-2y+2x-3y)`
`=(x+y)(5x-5y)=(x+y)*5(x-y)`
`g)` `(x^2+4)^2-16x^2`
`=(x^2+4)^2-(4x)^2`
`=(x^2+4-4x)(x^2+4+4x)`
`=(x^2-4x+4)(x^2+4x+4)`
`=(x-2)^2(x+2)^2`
`h)` `(x+y)^2-2(x+y)+1`
`=(x+y)^2-2(x+y)*1+1^2`
`=(x+y-1)^2`
`k)` `x^2+2x+1-y^2+2y-1`
`=x^2+2x+1-(y^2-2y+1)=(x+1)^2-(y-1)^2`
`=[(x+1)-(y-1)][(x-1)+(y-1)]`
`=(x-1-y+1)(x-1+y-1)`
`=(x-y)(x+y-2)`.
