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) M + (5x² - 2xy) = 6x² + 9xy - y²

=> M = (6x² + 9xy - y²) - (5x² - 2xy)

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

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

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

=> m = 25x²y - 13xy² + y³ - 11x²y + 2y³ = 14x²y - 13xy² + 3y³

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

a,\(M+\left(5x^2-2xy\right)=6x^2+9xy-y^2\) 

\(< =>M=6x^2+9xy-y^2-5x^2+2xy\)

\(< =>M=x^2+11xy-y^2\)

b,\(\left(25x^2y-13xy^2+y^3\right)-M=11x^2y-2y^3\)

\(< =>M=25x^2y-13xy^2+y^3-11x^2y+2y^3\)

\(< =>M=14x^2y-12xy^2+3y^3\)

c,\(M+\left(12x^4-15x^2y+2xy^2+7\right)=0\)

\(< =>M=15x^2y-7-2xy^2-12x^4\)

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

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

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

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

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

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

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

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

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

a) Ta có: \(M=x^2y+xy^2-5x^2y^2+x^3-2x^2y+6xy^2\)

\(=\left(x^2y-2x^2y\right)+\left(xy^2+6xy^2\right)-5x^2y^2+x^3\)

\(=x^3-x^2y+7xy^2-5x^2y^2\)

Bậc là 4

Ta có: \(N=3x^3+xy+y^2-x^2y^2-2-2xy+7y^2\)

\(=3x^3+\left(xy-2xy\right)+\left(y^2+7y^2\right)-x^2y^2-2\)

\(=3x^2+8y^2-xy-x^2y^2-2\)

Bậc là 4

\(a.M+(5x^2-2xy)=6x^2+9xy-y^2 \)
\(M=(6x^2+9xy-y^2)-(5x^2-2xy)\)
\(M=6x^2+9xy-y^2-5x^2+2xy\)
\(M=(6x^2-5x^2)+(9xy+2xy)-y^2\)
\(M=x^2+11xy-y^2\)
Vậy \(M=x^2+11xy-y^2\)
\(b.M+(3x^2y-2xy^3)=2x^2y-4xy^3\)
\(M=(2x^2y-4xy^3)-(3x^2-2xy^3)\)
\(M= \) \(2x^2-4xy^3-3x^2+2xy^3\)
\(M=(2x^2-3x^2)+(-4xy^3+2xy^3)\)
\(M=-x^2-2xy^3\)
Vậy \(M=-x^2-2xy^3\)

Mình sẽ giúp bạn bài này a. M+(5x^2-2xy) = 6x^2+9xy-y^2 M = (6x^2+9xy-y^2) - (5x^2-2xy) = 6x^2+9xy-y^2-5x^2+2xy = (6x^2-5x^2)+(9xy+2xy)+(-y^2) = x^2+11xy-y^2 b. M + (3x^2y−2xy^3)=2x^2y−4xy^3 M = (2x^2y−4xy^3)-(3x^2y−2xy^3) = 2x^2y−4xy^3-3x^2y+2xy^3 = (2x^2y-3x^2y)+(−4xy^3+2xy^3) = -x^2y+(-2xy^3) c.(1/2xy^2+x^2−x^2y)−M=−xy^2+x^2y+1 M =(1/2xy^2+x^2−x^2y)-(−xy^2+x^2y+1) =1/2xy^2+x^2−x^2y-xy^2-x^2y-1 = (1/2xy^2-xy^2)+(x^2y-x^2y)+x^2-1 = -1/2xy^2+x^2-1 d. M−(x^3.y^2−x^2.y+xy)=2x^3.y^2−3/2xy M= (2x^3.y^2−3/2xy)+(x^3.y^2−x^2.y+xy) = 2x^3.y^2−3/2xy+x^3.y^2−x^2.y+xy = (2x^3.y^2+x^3.y^2)+(3/2xy+xy)-x^2.y = 3x^3.y^2+5/2xy-x^2.y

a) M + (5x\(^2\) - 2xy) = 6x\(^2\) + 9xy - y\(^2\)

=> M = (6x\(^2\) + 9xy - y\(^2\)) - (5x\(^2\) - 2xy)

M = 6x\(^2\) + 9xy - y\(^2\) - 5x\(^2\) + 2xy

M = (6x\(^2\) - 5x\(^2\)) + (9xy + 2xy) - y\(^2\)

M = 1x\(^2\) + 11xy - y\(^2\)

làm ơn giúp e vs

\(1,=\left(x-2\right)\left(5-y\right)\\ 2,=2\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(2x-2y-z\right)\\ 3,=5xy\left(x-2y\right)\\ 4,=3\left(x^2-2xy+y^2-4z^2\right)=3\left[\left(x-y\right)^2-4z^2\right]\\ =3\left(x-y-2z\right)\left(x-y+2z\right)\\ 5,=\left(x+2y\right)^2-16=\left(x+2y-4\right)\left(x+2y+4\right)\\ 6,=-\left(6x^2-3x-4x+2\right)=-\left(2x-1\right)\left(3x-2\right)\\ 7,=\left(2x+y\right)\left(2x+y+x\right)=\left(2x+y\right)\left(3x+y\right)\\ 8,=\left(x-y\right)\left(x+5\right)\\ 9,=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\\ 10,=\left(x^2-9\right)x=x\left(x-3\right)\left(x+3\right)\\ 11,=\left(x-2\right)\left(y+1\right)\\ 12,=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\\ 13,=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x-y\right)\)

Bài 26:

\(A+B+C=4x^2-5xy+3y^2+3x^2+2xy+y^2-x^2+3xy+2y^2\)

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

\(=6x^2+6y^2\)

\(B-C-A=\left(3x^2+2xy+y^2\right)-\left(-x^2+3xy+2y^2\right)-\left(4x^2-5xy+3y^2\right)\)

\(=3x^2+2xy+y^2+x^2-3xy-2y^2-4x^2+5xy-3y^2\)

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

\(=-4xy-2y^2\)

\(C-A-B=\left(-x^2+3xy+2y^2\right)-\left(4x^2-5xy+3y^2\right)-\left(3x^2+2xy+y^2\right)\)

\(=-x^2+3xy+2y^2-4x^2+5xy-3y^2-3x^2-2xy-y^2\)

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

\(=-8x^2+6xy-2y^2\)