Đáp án: 4)`(x-y)^2+4(x-y)-12=(x−y−2)(x−y+6)`
5) `(x-1)(x-3)(x-5)(x-7)-20=(x^2-8x+5)(x^2-8x-3)`
6) `6x^4−11x^2+3=(3x^2−1)(2x^2−1)`
Giải thích các bước giải:
4. `(x-y)^2+4(x-y)-12`
Đặt `x−y=z`, có:
`z^2+4z−12=z^2+6z−2z−12`
`=(z^2−2z)+(6z−12)`
`=z(z−2)+6(z−2)`
`=(z−2)(z+6)`
Thay `z=x−y` ,ta được: `(x−y−2)(x−y+6)`
5. `(x-1)(x-3)(x-5)(x-7)-20`
`=[(x-1)(x-7)][(x-3)(x-5)]-20`
`=(x^2-8x+7)(x^2-8x+15)-20`
Đặt `x^2-8x+7=t`, ta có:
`t(t+8)-20`
`=t^2+8t-20`
`=t^2-2t+10t-20`
`=t(t-2)+10(t-2)`
`=(t-2)(t+10)`
`=(x^2-8x+7-2)(x^2-8x+7-10)`
`=(x^2-8x+5)(x^2-8x-3)`
6. `6x^4−11x^2+3`
`=6x^4−2x^2−9x^2+3`
`=2x^2(3x^2−1)−3(3x^2−1)`
`=(3x^2−1)(2x^2−1)`
