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a) \(xy+y-2x-2\)
\(=y\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(y-2\right)\)
b) \(xy+1+x+y\)
\(=y\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(y+1\right)\)
c) \(x\left(x-1\right)+y\left(x-1\right)+z\left(x-1\right)\)
\(=\left(x-1\right)\left(x+y+z\right)\)
a, \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)\(=x^2y+xy^2+y^2z+yz^2+x^2z+xz^2+2xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z\right)\)
\(=x\left(x+y+z\right)\left(y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+z\right)+y\left(x+z\right)\right]\)
\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)
b, \(2x^2+2y^2-x^2z+z-y^2z-2\)
\(=\left(2x^2-x^2z\right)+\left(2y^2-y^2z\right)-\left(2-z\right)\)
\(=x^2\left(2-z\right)+y^2\left(2-z\right)-\left(2-z\right)\)
\(=\left(2-z\right)\left(x^2+y^2-1\right)\)
Câu a:
Cách 1:
\(xy+y-2x-2\)
\(\Leftrightarrow\left(xy+y\right)-\left(2x+2\right)\)
\(\Leftrightarrow y\left(x+1\right)-2\left(x+1\right)\)
\(\Leftrightarrow\left(x+1\right)\left(y-2\right)\)
Cách 2:
\(xy+y-2x-2\)
\(\Leftrightarrow\left(xy-2x\right)+\left(y-2\right)\)
\(\Leftrightarrow x\left(y-2\right)+\left(y-2\right)\)
\(\Leftrightarrow\left(x+1\right)\left(y-2\right)\)
a)xy+y-2x-2
y(x + 1) - 2(x + 1)
<=> (y - 2)(x + 1)
b) x + x + x + 1
<=> 3x + 1
c)x3-3x2+3x-9
<=>(x - 3 ) 3
d)xy+xz+y2+yz
<=> x(y + z) + y(y + z)
<=> (x + y)(y + z)
f)x2+xy+xz-x-y-z
<=> x(x - y -z +1
a) \(xy+y-2x-2\)
\(=y\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(y-2\right)\)
b) \(xy+1+x+y\)
\(=y\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(y+1\right)\)
c) \(x^2+xy-x-y+xz-z\)
\(=\left(x^2-x\right)+\left(xy-y\right)+\left(xz-z\right)\)
\(=x\left(x-1\right)+y\left(x-1\right)+z\left(x-1\right)\)
\(=\left(x-1\right)\left(x+y+z\right)\)