a,x mũ 4+6x mũ 2y+9y mũ 2-1 b,3x mũ 2-6xy+3y mũ 2-12z mũ 2 c,a mũ 3-a mũ 2b-ab mũ 2 +b mũ3 d,8x mũ3+4x mũ 2-y mũ 3-y mũ2 03/07/2021 Bởi Maya a,x mũ 4+6x mũ 2y+9y mũ 2-1 b,3x mũ 2-6xy+3y mũ 2-12z mũ 2 c,a mũ 3-a mũ 2b-ab mũ 2 +b mũ3 d,8x mũ3+4x mũ 2-y mũ 3-y mũ2
Đáp án: `a) x^4+6x^2y+9y^2-1` `=(x^2+3y)^2-1` `=(x^2+3y-1)(x^2+3y+1)` `b) 3x^2-6xy+3y^2-12z^2` `=3(x^2-2xy+y^2-4z^2)` `=3[(x-y)^2-(2z)^2]` `=3(x-y-2z)(x-y+2z)` `c) a^3-a^2b-ab^2+b^3` `=a^2(a-b)-b^2(a-b)` `=(a-b)(a^2-b^2)` `=(a-b)^2(a+b)` `d) 8x^3+4x^2-y^3-y^2` `=(8x^3-y^3)+(4x^2-y^2)` `=(2x-y)(4x^2+2xy+y^2)+(2x-y)(2x+y)` `=(2x-y)(4x^2+2xy+y^2+2x+y)` Bình luận
Đáp án:
`a) x^4+6x^2y+9y^2-1`
`=(x^2+3y)^2-1`
`=(x^2+3y-1)(x^2+3y+1)`
`b) 3x^2-6xy+3y^2-12z^2`
`=3(x^2-2xy+y^2-4z^2)`
`=3[(x-y)^2-(2z)^2]`
`=3(x-y-2z)(x-y+2z)`
`c) a^3-a^2b-ab^2+b^3`
`=a^2(a-b)-b^2(a-b)`
`=(a-b)(a^2-b^2)`
`=(a-b)^2(a+b)`
`d) 8x^3+4x^2-y^3-y^2`
`=(8x^3-y^3)+(4x^2-y^2)`
`=(2x-y)(4x^2+2xy+y^2)+(2x-y)(2x+y)`
`=(2x-y)(4x^2+2xy+y^2+2x+y)`