Phân tích thành nhân tử: a) x4 – y4 b) x2 – 3y2 c) (3x – 2y)2 – (2x – 3y)2 d) 9(x – y)2 – 4(x + y)2 e) (4x2 – 4x + 1) – (x + 1)2 f) x3 + 27 g) 27x3 – 0,001 h) 125x3 – 1

Đáp án:

Giải thích các bước giải:

Đáp án:`+`Giải thích các bước giải:

`a)x^4-y^4`

`=(x-y)(x+y)(x^2+y^2)`

`b)x^2-3y^2`

`=x^2-(√3.y)^2`

`=(x-√3.y).(x+√3.y)`

`c)(3x–2y)^2–(2x–3y)^2`

`=(3x-2y+3x+3y)(3x-2y-2x+3y)`

`=(5x+y)(x+y)`.

`d)9(x – y)^2 – 4(x + y)^2`

`=[3(x-y)]^2–[2(x+y)]^2`

`=(3x-3y)^2-(2x+2y)^2`

`=(3x-3y-2x-2y)(3x-3y+2x+2y)`

`=(x-5y)(5x-y)`

`e)(4x^2–4x+1)–(x+1)^2`

`=4x^2−4x+1−1(x^2+2x+1)`

`=4x^2−4x−1x^2−2x`

`=3x^2−4x−2x`

`=3x^2−6x`

`=3(x^2−2x)`

`=3(x−2)x`

`f)x^3+27=x^3+3^3=(x+3)(x^2-3x+9)`

`g)``27x^3–0,001`

`=(3x)^3–(0,1)^3`

`=(3x–0,1).((3x)^2+3x.0,1+0,1)`

`=(3x–0,1)(9x^2+0,3x+0,01)`

`h)125x^3 – 1`

`=5x^3+1x^3`

`=(5x+1)(25x^2-5x+1)`