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

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

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

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

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

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

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

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

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

\(N=10xy-4y^2+7x^2\)

a) Có:

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

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

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

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

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

b) Có:

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

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

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

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

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

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

Chúc bạn học tốt!

Bài 1:

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

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

Bài 2:

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

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

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

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

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

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

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

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

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

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

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

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

Bài 3: 

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

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

Bài 2: 

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

\(A-B=4x^4-5xy+5y^2-3x^2-2xy+y=4x^4-3x^2+5y^2-7xy+y\)

\(B-A=-\left(A-B\right)=-4x^4+3x^2-5y^2+7xy-y\)

Lời giải:

Nếu $a\neq 0$ thì đa thức $M$ có bậc là $12+3=15\neq 5$ (trái với đề bài)

Nếu $a=0$ thì $M=-2xy+6x^3y^2$ có bậc $3+2=5$ (thỏa mãn)

Vậy $a=0$

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$N=-3xy^4+6x^3y^7+(a+1)x^3y^7-7xy$

$=-3xy^4+(a+7)x^3y^7-7xy$

Nếu $a+7\neq 0$ thì bậc của $N$ là $3+7=10\neq 5$ (trái đề)

Nếu $a+7=0$ thì $N=-3xy^4-7xy$ có bậc $1+4=5$ (thỏa đề)

Vậy $a+7=0\Leftrightarrow a=-7$

Ta có: \(M=x^2+y^2-2xy^2-6x^2-3xy^2\)

    \(\Rightarrow M=-5x^2+y^2-5xy^2\)