`***`Lời giải`***`
a)
`x^6-y^6`
`=(x^3)^2-(y^3)^2`
`=(x^3-y^3)(x^3+y^3)`
*Áp dụng: `A^2-B^2=(A+B)(A-B)`
b)
`x^4+2x^2y+y^2`
`=(x^2)^2+2x^2y+y^2`
`=(x^2+y)^2`
*Áp dụng: `(A+B)^2=A^2+2AB+B^2`
c)
`(x^2+1)^2-4x^2`
`=(x^2+1)^2-(2x)^2`
`=(x^2+1-2x)(x^2+1+2x)`
`=(x-1)^2(x+1)^2`
*Áp dụng: `(A+B)^2=A^2+2AB+B^2`
`(A-B)^2=A^2-2AB+B^2`
`A^2-B^2=(A+B)(A-B)`
d)
`1-(x^2-2xy+y^2)`
`=1^2-(x-y)^2`
`=(1+x-y)(1-x+y)`
*Áp dụng: `A^2-B^2=(A+B)(A-B)`
`(A-B)^2=A^2-2AB+B^2`
e)
`4x^2+81`
`=(2x)^2+9^2+36x-36x`
`=[(2x)^2+36x+9^2]-36x`
`=(2x+9)^2-(6\sqrt{x} )^2`
`=(2x+9-6\sqrt{x})(2x+9+6\sqrt{x})`
*Áp dụng: `A^2-B^2=(A+B)(A-B)`
`(A+B)^2=A^2+2AB+B^2`