a: \(=\left(4xy^2+2xy^2\right)+\left(3x^2y-3x^2y\right)=6xy^2\)

b: \(=xy\left(\dfrac{1}{5}+\dfrac{1}{3}\right)+xy^2\left(\dfrac{4}{3}-\dfrac{2}{5}\right)=\dfrac{8}{15}xy+\dfrac{14}{15}xy^2\)

d: \(=\dfrac{-4}{9}\cdot\dfrac{3}{2}\cdot xy^2\cdot xy^3=-\dfrac{2}{3}x^2y^5\)

đề bài là rút gọn à

a) M + (5x² - 2xy) = 6x² + 9xy - y²

=> M = (6x² + 9xy - y²) - (5x² - 2xy)

=> M = 6x² + 9xy - y² - 5x² + 2xy = (6x² - 5x²) + (9xy + 2xy) - y² = x² + 11xy - y²

b) Sửa đề lại đi nhé

c) (25x²y - 13x²y + y³) - M = 11x²y - 2y²

=> M = (25x²y - 13x²y + y³) - (11x²y - 2y²)

=> M = 25x²y - 13x²y + y³ - 11x²y + 2y²

=> M = x²y + y³ + 2y²

d) M = 0 - (12x⁴ - 15x²y + 2xy² + 7) = -12x⁴ + 15x²y - 2xy² - 7

a) Ta có : M = 6x² + 9xy - y² - (5x² - 2xy)

                    =  6x² + 9xy - y² - 5x² + 2xy

                    = x² + 11xy - y²

b) Ta có M = x² - 7xy + 8y² - (3xy - 24y²)

                 = x² - 7xy + 8y² - 3xy + 24y²

                  = x² - 10xy + 32y²

c) Ta có M = 25x².y- 13x²y + y³ - (11x²y - 2y²)

                  = 25x².y- 13x²y + y³ - 11x²y + 2y²

                 = x²y + y³ + 2y²

d) Ta có M = -(12x⁴ - 15x²y + 2xy² + 7)

                 =  -12x⁴ + 15x²y - 2xy² - 7

Yêu cầu là gì v c.

`@` `\text {Ans}`

`\downarrow`

`1)`

`x^3 - 2x - 1`

`= x^3 - x^2 - x + x^2 - x - 1`

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

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

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

`2)`

`x^3 +3x^2 -4`

`= x^3 + 4x^2 + 4x - x^2 - 4x - 4`

`= (x^3 + 4x^2 + 4x) - (x^2 + 4x + 4)`

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

`= (x-1)(x^2 + 4x + 4)`

`3)`

`x^3y^3 + x^2y^2 + 4`

`= x^3 y^3 - x^2y^2 + 2x^2y^2 + 2xy - 2xy + 4`

`= (x^3y^3 - x^2y^2 + 2xy) + (2x^2y^2 - 2xy + 4)`

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

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

`4)`

`x^3 + 5x^2 -9xy^2+5y^3`

Bạn xem lại đề ;-;

`5)`

` x^4 + x^3 + 6x^2 + 5x + 5`

`= x^4 + x^3 + 5x^2 + x^2 + 5x + 5`

`= (x^4 + x^3 + x^2) + (5x^2 + 5x + 5)`

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

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

a)\(9y^3-y\)

\(=y\left(9y^2-1\right)\)

\(=y\left(3y-1\right)\left(3y+1\right)\)

\(9y^3-y=y\left(9y^2-1\right)=y\left(3y+1\right)\left(3y-1\right)\)

\(8y^3-2y\left(1-2y\right)^2=2y\left[\left(2y\right)^2-\left(1-2y\right)^2\right]=2y\left(4y-1\right)\)

\(2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\)

\(2x^4-6x^3+6x^2-2x=2x\left(x^3-3x^2+3x-1\right)=2x\left(x-1\right)^3\)\(x^3-8x^2+8x=x\left(x^2-8x+8\right)\)

\(5x^4-15x^3y+15x^2y^2-5xy^3-5x=5x\left(x^3-3x^2y+3xy^2-y^3-1\right)=5x\left[\left(x-y\right)^3-1\right]=5x\left(x-y-1\right)\left(x^2-2xy+y^2+x-y+1\right)\)

MINH CUNG VAY

Tìm đa thức M biết :

a, M +5 (5x² - 2xy) = 6x² +9xy - y²

M + 5. 5x² - 5. 2xy = 6x² + 9xy - y²

M + 25x² - 10xy = 6x² + 9xy - y²

M = 6x² + 9xy - y² + 10xy - 25x²

M = ( 6x² - 25x² ) + ( 9xy + 10xy ) - y²

M = -19x² + 19xy - y²

b, M - ( 3xy - 4y² ) = x² - 7xy + 8xy

M - 3xy + 4y² = x² - 15xy

M = x² - 15xy - 4y² + 3xy

M = x² + ( 15xy + 3xy ) - 4y²

M = x² + 18xy - 4y²

c, (25 . x²y - 13xy²+ y³ ) - M = 11x²y - 2y³

25x²y - 13xy²+ y³ - M = 11x²y - 2y³

M = 25x²y - 13xy²+ y³ - 11x²y - 2y³

M = ( 25x²y - 11x²y ) + ( y³ - 2y³ ) - 13xy²

M = 14x²y - y³ - 13xy²

d, M + (5x² - 2xy )= 6x² + 9xy -y²

M + 5x² - 2xy = 6x² + 9xy -y²

M = 6x² + 9xy -y² + 2xy - 5x²

M = ( 6x² - 5x² ) + ( 9xy + 2xy ) - y²

M = x² + 11xy - y²

a: \(=\dfrac{2xy\left(2x^2y-4x+5\right)}{2xy}=2x^2y-4x+5\)

b: \(=\dfrac{x^2y\left(7x^2y-2y-5x^2y^3\right)}{3x^2y}=\dfrac{7}{3}x^2y-\dfrac{2}{3}y-\dfrac{5}{3}x^2y^3\)