Đáp án:
`a)(x^2+2xy+2y^2)(x^2-2xy+2y^2)`
`b)(2x^2+6x+9)(2x^2-6x+9)`
`c)(x-5y)(x+y)`
`d)(x^2+x+1)(x^3-x^2+1)`
Giải thích các bước giải:
`a)x^4+4y^4`
`=x^4+4x²y²-4x²y²+4y^4`
`=(x^4+4x²y²+4y^4)-4x²y²`
`=[(x^2)^2+2.x².2y²+(2y^2)^2]-4x²y²`
`=(x^2+2y^2)^2-(2xy)^2`
`=(x^2+2xy+2y^2)(x^2-2xy+2y^2)`
`b)4x^4+81`
`=4x^4+36x^2-36x^2+81`
`=(4x^4+36x^2+81)-36x^2`
`=[(2x^2)^2+2.2x².9+9²]-36x^2`
`=(2x^2+9)^2-(6x)^2`
`=(2x^2+6x+9)(2x^2-6x+9)`
`c)x²-4xy-5y²`
`=x²-5xy+xy-5y²`
`=(x²-5xy)+(xy-5y²)`
`=x(x-5y)+y(x-5y)`
`=(x-5y)(x+y)`
`d)x^5+x+1`
`=x^5+x^2-x^2+x+1`
`=(x^5-x^2)+(x^2+x+1)`
`=x^2(x^3-1)+(x^2+x+1)`
`=x^2(x-1)(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1)[x^2(x-1)+1]`
`=(x^2+x+1)(x^3-x^2+1)`
