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Sửa đề : \(\frac{1-3x}{2x}+\frac{3x-2}{2x-1}+\frac{3x-2^2}{4x^2-2x}\)
\(=\frac{\left(1-3x\right)\left(2x-1\right)}{2x\left(2x-1\right)}+\frac{2x\left(3x-2\right)}{2x\left(2x-1\right)}+\frac{3x-4}{2x\left(2x-1\right)}\)
\(=\frac{2x-1-6x+3x+6x^2-4x+3x-4}{2x\left(2x-1\right)}\)
\(=\frac{-2x+6x^2-5}{2x\left(2x-1\right)}\)
Thay x = 1/234 vào tính là ra giá trị biểu thức nhé !!!
a/ \(x^2-5x+5y-y^2=\left(x^2-y^2\right)-\left(5x-5y\right)=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
b/ \(3x^2-6xy+3y^2-12z^2=3\left(x^2-2xy+y^2-4z^2\right)=3\left[\left(x^2-2xy+y^2\right)-\left(2x\right)^2\right]=3\left[\left(x-y\right)^2-\left(2x\right)^2\right]=3\left(x-y-2x\right)\left(x-y+2x\right)=3\left(-x-y\right)\left(3x-y\right)\)
c/ \(x^2-2xy+y^2-xz+yz=\left(x^2-2xy+y^2\right)-\left(xz-yz\right)=\left(x-y\right)^2-z\left(x-y\right)=\left(x-y\right)\left(x-y-z\right)\)
d/ \(x^2-x+2y-4y^2=\left(x^2-4y^2\right)-\left(x+2y\right)=\left(x+2y\right)\left(x-2y\right)-\left(x+2y\right)=\left(x+2y\right)\left(x-2y-1\right)\)
e/ \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
a) x2 - 5x + 5y - y2
= ( x2 - y2 ) - ( 5x - 5y )
= ( x - y )( x + y ) - 5( x - y )
= ( x - y )( x + y - 5 )
b) 3x2 - 6xy + 3y2 - 12z2
= 3( x2 - 2xy + y2 - 4z2 )
= 3[( x2 - 2xy + y2 ) - 4z2 ]
= 3[( x - y )2 - 4z2 ]
= 3( x - y - 2z )( x - y + 2z )
c) x2 - 2xy + y2 - xz - yz
= ( x2 - 2xy + y2 ) - ( xz - yz )
= ( x - y )2 - z( x - y )
= ( x - y )( x - y - z )
d) x2 - x + 2y - 4y2
= ( x2 - 4y2 ) - ( x - 2y )
= ( x - 2y )( x + 2y ) - ( x - 2y )
= ( x - 2y )(x + 2y - 1 )
e) x6 - y6
= ( x3 )2 - ( y3 )2
= ( x3 - y3 )( x3 + y3 )
= ( x - y )( x2 + xy + y2 )( x + y )( x2 - xy + y2 )
Chúc bạn học tốt 
a) \(\left(3x-5\right)\left(2x+3\right)-\left(2x-3\right)\left(3x+7\right)-2x\left(x-4\right)\)
\(=\left(6x^2-x-15\right)-\left(6x^2+5x-21\right)-\left(2x^2-8x\right)\)
\(=6x^2-x-15-6x^2-5x+21-2x^2+8x\)
\(=-2x^2+2x+6\)
\(=-2\left(x^2-x-3\right)\)
b) \(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^2-4\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^4-16\right)\)
\(=\left(x^4+4x^2+4\right)-\left(x^4-16\right)\)
\(=x^4+4x^2+4-x^4+16\)
\(=4x^2+20\)
\(=4\left(x^2+5\right)\)
c) \(\left(2x-y\right)^2-2\left(x+3y\right)^2-\left(1+3x\right)\left(3x-1\right)\)
\(=\left(4x^2-4xy+y^2\right)-2\left(x^2+6xy+9y^2\right)-\left(9x^2-1\right)\)
\(=4x^2-4xy+y^2-2x^2-16xy-18y^2-9x^2+1\)
\(=-7x^2-20xy-17y^2+1\)
d) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^6-3x^4+3x^2-1\right)-\left(x^6-1\right)\)
\(=x^6-3x^4+3x^2-1-x^6+1\)
\(=-3x^4+3x^2\)
\(=-3x^2\left(x^2-1\right)\)
\(=-3x^2\left(x-1\right)\left(x+1\right)\)
e) \(\left(2x-1\right)^2-2\left(4x^2-1\right)+\left(2x+1\right)^2\)
\(=\left(2x-1\right)^2-2\left(2x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)
\(=\left[\left(2x-1\right)-\left(2x+1\right)\right]^2\)
\(=\left(2x-1-2x-1\right)^2\)
\(=\left(-2\right)^2=4\)
g) \(\left(x-y+z\right)^2+\left(y-z\right)^2-2\left(x-y+z\right)\left(z-y\right)\)
\(=\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)
\(=\left(x-y+z+y+z\right)^2\)
\(=\left(x+2z\right)^2\)
h) \(\left(2x+3\right)^2+\left(2x+5\right)^2-\left(4x+6\right)\left(2x+5\right)\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\)
\(=\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\)
\(=\left(2x+3-2x-5\right)^2\)
\(=\left(-2\right)^2=4\)
i) \(5x^2-\dfrac{10x^3+15x^2-5x}{-5x}-3\left(x+1\right)\)
\(=5x^2-\dfrac{-5x\left(-2x^2-3x+1\right)}{-5x}-3\left(x+1\right)\)
\(=5x^2-\left(-2x^2-3x+1\right)-3\left(x+1\right)\)
\(=5x^2+2x^2+3x-1-3x-3\)
\(=7x^2-4\)
A=\(x^3-2x^2+x\)
=x.(x2-2x+1)
=x(x-1)2
B=\(2x^2+4x+2-2y^2\)
=\(2\left(x^2+2x+1-y^2\right)\)
=\(2.\left[\left(x+1\right)^1-y^2\right]\)
=\(2\left(x+1-y\right)\left(x+1+y\right)\)
C=\(2xy-x^2-y^2+16\)
=\(-\left(-2xy+x^2+y^2-16\right)\)
=\(-\left[\left(x-y\right)^2-4^2\right]\)
=-(x-y-4)(x-y+4)
D=\(x^3+2x^2y+xy^2-9x\)
=\(x\left(x^2+2xy-y^2-9\right)\)
=\(x.\left[\left(x-y\right)^2-3^2\right]\)
=x.(x-y-3)(x-y+3)
E=\(2x-2y-x^2+2xy-y^2\)
\(=\left(2x-2y\right)-\left(x^2-2xy+y^2\right)\)
=\(2\left(x-y\right)-\left(x-y\right)\left(x-y\right)\)
=(x-y)(2x-2y-x+y)
=(x-y)(x+y)
z2 - (x-1)2 + 2(x-1) -1
= z2 - [ (x-1)2 - 2.(x-1).1 +12]
= z2 - (x-1-1)2
= z2- (x-2)2
= (z-x+2)(z+x-2)
`z^2 - (x-1)^2 + 2 (x-1)-1`
`= z^2 -[(x-1)^2 - 2 (x-1).1+1^2]`
`= z^2 - (x-2)^2`
`= (z-x+2)(z+x-2)`
Lời giải:
a. $A=9x^2+15x+6xy+y^2+5y=(9x^2+6xy+y^2)+(15x+5y)$
$=(3x+y)^2+5(3x+y)=0^2+5.0=0$
b. $25x^2-y^4-5x+y^2=(25x^2-y^4)-(5x-y^2)=(5x-y^2)(5x+y^2)-(5x-y^2)$
$=(5x-y^2)(5x+y^2-1)$