a: \(=\dfrac{2\left(x+2\right)\left(x-1\right)}{x+2}=2x-2\)

b: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)

c: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)

d: \(=\dfrac{x^2\left(x-3\right)}{x-3}=x^2\)

`@` `\text {Ans}`

`\downarrow`

`!`

`(x^3-3x^2):(x-3)`         

`= x^2(x-3)  :(x-3)` 

`=x^2`

`----`

`(2x^2+2x-4):(x+2)`

`=2(x^2+x-2) :(x+2)`

`= 2 (x^2+2x-x-2) :(x+2)`

\(=2\left[x\left(x+2\right)-\left(x+2\right)\right]:\left(x+2\right)\)

`= 2(x+2)(x-1) :(x+2)`

`=2(x-1)`

`-------`

`(x^4-x-14):(x-2)`

https://hoc24.vn/cau-hoi/x4-x-14-x-2-giup-minh.204306769717

bn tham khảo ở đây nha

`----`

`(x^3-3x^2+x-3):(x-3)`

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

`=(x-3)(x^2+1):(x-3)`

`=x^2+1`

a: \(=\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)

\(=\dfrac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)

\(=2x^2+x+1\)

b: \(=\dfrac{x^5+x^2+x^3+1}{x^3+1}=x^2+1\)

c: \(=\dfrac{2x^3-x^2-x+6x^2-3x-3+2x+6}{2x^2-x-1}\)

\(=x+3+\dfrac{2x+6}{2x^2-x-1}\)

d: \(=\dfrac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)

\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5}{3x^2-2x+1}\)

\(=x^2-2x-5\)

a)\(x^3y+3x^2y\)

b)\(-24x^2+4xy\)

[9x3(x2-1)-6x2(x2-1)2+12x(x2-1)]:3x(x2-1)

Gọi x2-1 là y tá đc

(9x3y-6x2y2+12xy):3xy

=3x2-2xy+4

=3x2-2x(x2-1)+4

\(\left(x-2\right)\left(x^2-5x+1\right)-x\left(x^2+11\right)=x^3-5x^2+x-2x^2+10x-2-x^3-11x=-7x^2-2\)

\(\left(3x^2-2x+1\right)\left(x^2+2x+3\right)-4x\left(x^2-1\right)-3x^2\left(x^2+2\right)=3x^4+6x^3+9x^2-3x^3-4x^2-6x-4x^3+4x-3x^4-6x^2=0\)

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}\)

\(\text{=}\dfrac{-1}{15}+\dfrac{1}{5}+\dfrac{2}{45}\)

\(\text{=}\dfrac{8}{45}\)

Áp dụng tính chất đổi dấu và giao hoán của phép nhân phân số, ta có:

\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}=\dfrac{1}{5}.\dfrac{-3}{9}+\dfrac{1}{5}.\dfrac{4}{4}+\dfrac{1}{5}.\dfrac{2}{9}\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+1+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}\left(-\dfrac{3}{9}+\dfrac{9}{9}+\dfrac{2}{9}\right)\)

                                           \(=\dfrac{1}{5}.\dfrac{8}{9}\)

                                           \(=\dfrac{8}{45}\)

\(x^2-3x+xy-3x\)

\(=x^2+xy-6x\)

\(=x.\left(x+y-6\right)\)

1) \(x\left(x+4\right)\left(x-4\right)-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x\left(x^2-16\right)\)

\(=x^3-16x-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x^3-16x-x^4+1\)

b) \(7x\left(4y-x\right)+4y\left(y-7x\right)-2\left(2y^2-3.5x\right)\)

\(=28xy-7x^2+4y\left(y-7x\right)-2\left(2y^2-3.5x\right)\)

\(=28xy-7x^2+4y^2-28xy-4y^2+7x\)

\(=-7x^2+7x\)

c) \(\left(3x-1\right)\left(2x-5\right)-4\left(2x^2-5x+2\right)\)

\(=6x^2-17x+5-4\left(2x^2-5x+2\right)\)

\(=6x^2-17x+5-8x^2+20x-8\)

\(=-2x^2+3x-3\)

a)  x(x+4)(x-4)-(x²+1)(x²-1)

=>x(x²-4²)-(x⁴-1²)

=>x³-16x-x⁴+1

=>-x⁴-x³-15x

b)  7x(4y-x)+4y(y-7x)-2(2y²-3.5x)

=>28xy-7x²+4y²-28xy-4y²+30x

=>-7x²+30x

c)  (3x+1)(2x-5)-4(2x²-5x+2)

=>6x²-15x+2x-5-8x²+20x-8

=>-2x²+7x-13