Bài 1: 

\(M=6x^2+xyz+2xy+3-y^2+3xyz-5x^2+7xy-9\)

\(=x^2+4xyz+9xy-y^2-6\)

Bài 2: 

a: Sửa đề: \(x^2+2x+3\)

Đặt \(x^2+2x+3=0\)

\(\Delta=2^2-4\cdot1\cdot3=4-12=-8< 0\)

Do đó: Phương trình vô nghiệm

b: Đặt \(x^2+4x+6=0\)

\(\Leftrightarrow x^2+4x+4+2=0\)

\(\Leftrightarrow\left(x+2\right)^2+2=0\)(vô lý)

a/

 \(M+5x^2-2xy-6x^2-9xy+y^2=0\)

\(M-x^2-11xy+y^2=0\)

\(M-x^2+y^2-11xy=0\)

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

Vậy:..

Câu b tương tự

M + (5x² - 2xy) = 6x² + 9xy - y^{2   ta có} M = ( 6x² + 9xy - y^{2) -(}5x² - 2xy)= x2 +11xy -y2

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

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

\(N=3xy-4y^2-x^2+7xy-8y^2\)

\(N=-x^2+10xy-12y^2\)

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

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

b.     \(\left(3xy-4y^2\right)-N=x^2-7xy+8y^2\)

\(\Rightarrow N=3xy-4y^2-x^2+7xy-8y^2\)

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

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: \(M=6x^2+9xy-y^2-5x^2+2xy=x^2+11xy-y^2\)

b: \(N=3xy-4y^2-x^2+7xy-8y^2=-x^2+10xy-12y^2\)

C= x² y - \(\dfrac{1}{2}\)xy² + \(\dfrac{1}{3}\)x²y +\(\dfrac{2}{3}\)xy² + 1

C=(x²y + \(\dfrac{1}{3}\)x²y )+( - \(\dfrac{1}{2}\)xy² +\(\dfrac{2}{3}\)xy²)+ 1

C=\(\dfrac{4}{3}\)x²y +\(\dfrac{1}{6}\)xy²+1

=>Bặc: 3

D= xy²z + 3xyz² - \(\dfrac{1}{5}\)xy²z - \(\dfrac{1}{3}\)xyz² - 2

D=(xy²z - \(\dfrac{1}{5}\)xy²z )+( 3xyz² - \(\dfrac{1}{3}\)xyz²) - 2

D=\(\dfrac{4}{5}\)xy²z +\(\dfrac{8}{3}\)xyz² - 2

=> Bậc :4

E = 3xy⁵ - x²y + 7xy - 3xy⁵ + 3x²y - \(\dfrac{1}{2}\)xy + 1

E=(3xy⁵- 3xy⁵) + (- x²y + 3x²y) + (7xy - \(\dfrac{1}{2}\)xy)+ 1

E= 2x²y + \(\dfrac{13}{2}\)xy + 1

=> Bậc: 3

K = 5x³ - 4x + 7x² - 6x³ + 4x + 1

K= (5x³ - 6x³ ) + (- 4x + 4x) +1

K= -1x³ + 1

=>Bậc: 3

F = 12x³y² - \(\dfrac{3}{7}\)x⁴y² + 2xy³ - x³y² + x⁴y² - xy³ - 5

F=( 12x³y² - x³y²) + (- \(\dfrac{3}{7}\)x⁴y² + x⁴y²) + (2xy³ - xy³) -5

F=11x³y² + \(\dfrac{4}{7}\)x⁴y² + xy³ - 5

=> Bậc :6

CHÚC BN HỌC TỐT ^-^