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12 tháng 8 2015
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
ML
12 tháng 8 2015
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
12 tháng 8 2015
c) 2x^3y - 2xy^3 - 4xy^2 - 2xy
= 2xy ( x^2 - y^2 - 2y - 1 )
= 2xy ( x^2 - ( y^2 + 2y + 1 )
= 2xy ( x^2 - ( y + 1 )^2 )
= 2x ( x - y - 1 )( x + y + 1 )
1 tháng 10 2018
sai bạn ơi !
đáp án là
= 2xy (x + y + 1) (x - y + 1)
that pun cho ban Nguyen Dieu Thao :((
LT
3
21 tháng 6 2017
A = x2(x - 1) + 6(1 - x)
A = x3 - x2 + 6 - 6x
A = (x3 - 6x) - (x2 - 6)
A = x.(x2 - 6) - (x2 - 6)
A = (x - 1)(x2 - 6)
21 tháng 6 2017
C = x2 + 2xy + y2 - yz - xz
C = (x + y)2 - z.(x + y)
C = (x + y - z).(x + y)
TA
16 tháng 7 2017
a) \(x^2+2x-4y^2-4y=\left(x^2-4y^2\right)+\left(2x-4y\right)=\left(x+2y\right)\left(x-2y\right)+2\left(x-2y\right)\)
\(=\left(x-2y\right).\left(x+2y+2\right)\)
b) \(x^4-6x^3+54x-81=\left(x^4-81\right)-\left(6x^3-54x\right)=\left(x^2-9\right)\left(x^2+9\right)-6x.\left(x^2-9\right)\)
\(=\left(x^2-9\right).\left(x^2+9-6x\right)=\left(x+3\right).\left(x-3\right).\left(x-3\right)^2=\left(x+3\right).\left(x-3\right)^3\)
c) \(ax^2+ax-bx^2-bx-a+b=\left(ax^2-bx^2\right)+\left(ax-bx\right)-\left(a-b\right)\)
\(=x^2.\left(a-b\right)+x.\left(a-b\right)-\left(a-b\right)=\left(a-b\right).\left(x^2+x-1\right)\)
d) \(\left(x^2+y^2-2\right)^2-\left(2xy-2\right)^2=\left(x^2+y^2-2+2xy-2\right).\left(x^2+y^2-2-2xy+2\right)\)
\(=\left(x^2+2xy+y^2-4\right).\left(x^2+y^2-2xy\right)=\left[\left(x+y\right)^2-4\right].\left(x-y\right)^2\)
\(=\left(x+y+2\right).\left(x+y-2\right).\left(x-y\right)^2\)
10 tháng 7 2018
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
AK
10 tháng 7 2018
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
KN
8 tháng 10 2020
a. x4 - 27x = x ( x3 - 33 ) = = x ( x - 3 ) ( x2 + 3x + 32 ) = x ( x - 3 ) ( x2 + 3x + 9 )
b. x3 + 2x2 + 2x + 1 = ( x3 + 13 ) + ( 2x2 + 2x ) = ( x + 1 ) ( x2 - x + 1 ) + 2x ( x + 1 ) = ( x + 1 ) ( x2 + x + 1 )
c. 4x - 4y + x2 - 2xy + y2 = 4 ( x - y ) + ( x - y )2 = ( x - y ) ( x - y + 4 )
8 tháng 10 2020
a
\(x^4-27x\)
\(=x\left(x^3-27\right)\)
\(=x\left(x^3-3^3\right)\)
\(=x\left(x-3\right)\left(x^2+3x+9\right)\)
b
\(x^3+2x^2+2x+1\)
\(=x^3+x^2+x^2+x+x+1\)
\(=x^2\left(x+1\right)+x\left(x+1\right)+1\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
c
\(4x-4y+x^2-2xy+y^2\)
\(=4\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(x-y+4\right)\)
8 tháng 6 2017
a) \(=x^2+2xy+y^2-x^2+y^2=2xy+2y^2=2y\left(x+y\right)\)
b) \(=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x+2y\right)\left(x-2y-2\right)\)
c) \(=3\left[\left(x^2+2xy+y^2\right)-z^2\right]=3\left[\left(x+y\right)^2-z^2\right]=3\left(x+y+z\right)\left(x+y-z\right)\)
d) \(=\left(2xy+1+2x+y\right)\left(2xy+1-2x-y\right)\)
e) \(=\left(x-3\right)\left(x^2+3x+9\right)-2x\left(x-3\right)=\left(x-3\right)\left(x^2+x+9\right)\)
f) \(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)=\left(x+5\right)\left(x^2-6x+25\right)\)
8 tháng 6 2017
a) \(\left(x+y\right)^2-\left(x^2-y^2\right)\)
\(=x^2+2xy+y^2-x^2+y^2\)
\(=2y^2+2xy\)
\(=2y\left(x+y\right)\)
c) \(3x^2+6xy+3y^2-3z^2\)
\(=3\left(x^2+2xy+y^2-x^2\right)\)
\(=3\left[\left(x+y\right)^2-z^2\right]\)
\(=3\left(x+y+z\right)\left(x+y-z\right)\)
d) \(\left(2xy+1\right)^2-\left(2x+y\right)^2\)
\(=\left(2xy+1+2x+y\right)\left(2xy+1-2x-y\right)\)
\(=\left[\left(2xy+2x\right)+\left(y+1\right)\right]\left[\left(2xy-2x\right)-\left(y-1\right)\right]\)
\(=\left[2x\left(y+1\right)+\left(y+1\right)\right]\left[2x\left(y-1\right)-\left(y-1\right)\right]\)
\(=\left(2x+1\right)\left(y+1\right)\left(2x-1\right)\left(y-1\right)\)
\(=\left(4x^2-1\right)\left(y^2-1\right)\)
b) x2 - 2x - 4y2 - 4y
= x2 - 2x + 1 - 4y2 - 4y - 1
= ( x - 1 )2 - [ ( 2y )2 + 2.2.y + 1 ]
= ( x - 1 )2 - ( 2y + 1 )2
= ( x - 1 + 2y + 1 ).( x - 1 - 2y - 1 )
= ( x + 2y ).( x - 2y - 2 )
Bài làm
a) xz - yz - x2 + 2xy - y2
= ( xz - yz ) - ( x2 - 2xy + y2 )
= z( x - y ) - ( x - y )2
= ( x - y )( z - x + y )
b) x2 - 2x - 4y2 - 4y
= x2 - 2x - 4y2 - 4y + 1 - 1
= ( x2 - 2x + 1 ) - ( 4y2 + 4y + 1 )
= ( x - 1 )2 - ( 2y + 1 )2
= ( x - 1 - 2y - 1 )( x - 1 + 2y + 1 )
= ( x - 2y - 2 )( x + 2y )
# Học tốt #