M=x²-2xy+y² N=y²+2xy+x²+1 Tính M+N và M-N
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a) \(\left\{{}\begin{matrix}M=x^2y-2xy+6-xy=x^2y-3xy+6\\N=-2x^2y+2xy+x^2y-3=-x^2y+2xy-3\end{matrix}\right.\)
b) \(x=1;y=2\Rightarrow M=1^2.2-2.1.2+6-1.2=2\)
c) \(M+N\Rightarrow x^2y-3xy+6+\left(-x^2y\right)+2xy-3=-xy+3\)
Bài 1:
e: Ta có: \(x\left(y-x\right)^2-x^2+2xy-y^2\)
\(=x\left(x-y\right)^2-\left(x-y\right)^2\)
\(=\left(x-y\right)^2\cdot\left(x-1\right)\)
Bài 2:
a: Ta có: \(M=m^2\left(m+n\right)-n^2m-n^3\)
\(=m^2\left(m+n\right)-n^2\left(m+n\right)\)
\(=\left(m+n\right)^2\cdot\left(m-n\right)\)
\(=\left(-2017+2017\right)^2\cdot\left(-2017-2017\right)\)
=0
M + N = \(x^2-2xy+y^2\)+\(y^2+2xy+x^2+1\)
= \(\left(x^2+x^2\right)+\left(-2xy+2xy\right)+\left(y^2+y^2\right)+1\)
= \(2x^2+2y^2+1\)
M - N = \(x^2-2xy+y^2-y^2+2xy+1\)
= \(\left(x^2+x^2\right)+\left(-2xy+2xy\right)+\left(y^2-y^2\right)+1\)
= \(2x^2+1\)
a/ M + N = x\(^2\)- 2xy + y\(^2\)+ y\(^2\)+ 2xy + x\(^2\)+ 1
= 2x\(^2\)+ 2y\(^2\)+ 1
= 2( x\(^2\)+ y\(^2\)) + 1
b/ M - N = x\(^2\)- 2xy + y\(^2\)- ( y\(^2\)+ 2xy + x\(^2\)+ 1 )
= x\(^2\)- 2xy + y\(^2\)- y\(^2\)- 2xy - x\(^2\)- 1
= -4xy - 1
\(M=x^2-2xy+y^2\)
\(N=y^2+2xy+x^2+1\)
\(a,M+N=\left(x^2-2xy+y^2\right)+\left(y^2+2xy+x^2+1\right)\)
\(=x^2-2xy+y^2+y^2+2xy+x^2+1\)
\(=\left(x^2+x^2\right)+\left(-2xy+2xy\right)+\left(y^2+y^2\right)+1\)
\(=2x^2+2y^2+1\)
\(b,M-N=\left(x^2-2xy+y^2\right)-\left(y^2+2xy+x^2+1\right)\)
\(=x^2-2xy+y^2-y^2-2xy-x^2-1\)
\(=\left(x^2-x^2\right)+\left(-2xy-2xy\right)+\left(y^2-y^2\right)-1\)
\(=-4xy-1\)
a, M + N = \(\left(x^2-2xy+y^2\right)+\left(y^2+2xy+x^2+1\right)\)
=\(2x^2+2y^2+1\)
b,M - N =\(\left(x^2-2xy+y^2\right)-\left(y^2+2xy+x^2+1\right)\)
=\(-4xy-1\)
\(M+N=2x^2+2y^2+1\)
\(M-N=x^2-2xy+y^2-x^2-2xy-y^2-1=-4xy-1\)