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1) \(5x^2-5xy-9x+9y\)
\(=5x\left(x-y\right)-9\left(x-y\right)\)
\(=\left(5x-9\right)\left(x-y\right)\)
2) \(m^3+4m^2+3m\)
\(=m^3+3m^2+m^2+3m\)
\(=m^2.\left(m+3\right)+m\left(m+3\right)\)
\(=\left(m^2+m\right)\left(m+3\right)\)
\(=m\left(m+1\right)\left(m+3\right)\)
3) \(x^2-2xy-15y^2\)
\(=x^2-2xy+y^2-16y^2\)
\(=\left(x-y\right)^2-\left(4y\right)^2\)
\(=\left(x-y-4y\right)\left(x-y+4y\right)\)
a) \(=\left(x-2y\right)\left(x^2+5x\right)\)
b) \(=\left(x-1\right)\left(x^2+2x+1\right)=\left(x-1\right)\left(x+1\right)^2\)
c) \(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(3-x+3\right)\)
\(=\left(x+3\right)\left(6-x\right)\)
e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)
f) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
\(a,y-x^2y+2xy^2-y^3=y(1-x^2+2xy-y^2) =y[1-(x^2-2xy+y^2)]=y[1-(x-y)^2] =y(1-x+y)(1+x-y) =y(x+y-1)(x-y+1) \)
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 )
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)
a) \(5ax-15ay+20a\)
\(=5a\left(x-3y+4\right)\)
b) \(6xy-12x-8y\)
\(=6\left(xy-2x-3y\right)\)
c) \(3ab\left(x-y\right)+3a\left(y-x\right)\)
\(=3a\left(x-y\right)\left(b-1\right)\)
d) \(x^2-xy+2x-2y\)
\(=\left(x+2\right)\left(x-y\right)\)
e) \(ax^2-5x^2-ax+5x+a-5\)
\(=\left(a-5\right)\left(x^2-x+1\right)\)
a, \(5ax-15ay+20a=5a\left(x-5y+4\right)\)
b, sai
c, \(3ab\left(x+y\right)+3a\left(y-x\right)=3ab\left(x+y\right)-3a\left(x+y\right)=\left(3ab-3a\right)\left(x+y\right)\)
d, \(x^2-xy+2x-2y=x\left(x+2\right)-y\left(x+2\right)=\left(x-y\right)\left(x+2\right)\)
Tượng tự ...
a) 5ax - 15ay + 20a = 5a( x - 3y + 4 )
b) 6xy - 12x - 8y = 2( xy - 6x - 4y )
c) 3ab( x - y ) + 3a( y - x ) = 3ab( x - y ) - 3a( x - y ) = ( x - y )( 3ab - 3a ) = 3a( x - y )( b - 1 )
d) x2 - xy + 2x - 2y = x( x - y ) + 2( x - y ) = ( x - y )( x + 2 )
e) ax2 - 5x2 - ax + 5x + a - 5 = x2( a - 5 ) - x( a - 5 ) + ( a - 5 ) = ( a - 5 )( x2 - x + 1 )
g) x2y - 4xy2 + 4y3 - 36yz2 = y( x2 - 4xy + 4y2 - 36z2 ) = y[ ( x2 - 4xy + 4y2 ) - 36z2 ] = y[ ( x - 2y )2 - ( 6z )2 ] = y( x - 2y - 6z )( x - 2y + 6z )
h) 4xy - x2 - 4y2 + m2 - 6m + 9
= ( m2 - 6x + 9 ) - ( x2 - 4xy + 4y2 )
= ( m - 3 )2 - ( x - 2y )2
= ( m - 3 - x + 2y )( m - 3 + x - 2y )
i) x2 + x - 12 = x3 - 3x + 4x - 12 = x( x - 3 ) + 4( x - 3 ) = ( x - 3 )( x + 4 )
k) 5x2 + 14x - 3 = 5x2 - x + 15x - 3 = x( 5x - 1 ) + 3( 5x - 1 ) = ( 5x - 1 )( x + 3 )
m) x2 - 5xy + 4y2 = x2 - xy - 4xy + 4y2 = x( x - y ) - 4y( x - y ) = ( x - y )( x - 4y ) < đã sửa đề >
n) 3x2 - 5xy + 2y2 + 4x - 4y = ( 3x2 - 5xy + 2y2 ) + ( 4x - 4y ) = ( 3x2 - 3xy - 2xy + 2y2 ) + 4( x - y ) = [ 3x( x - y ) - 2y( x - y ) ] + 4( x - y ) = ( x - y )( 3x - 2y ) + 4( x - y ) = ( x - y )( 3x - 2y + 4 )
f) 2x3 + 4x2y + 2xy2 = 2x( x2 + 2xy + y2 ) = 2x( x + y )2
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a, x3y - 9xy = xy(x2 - 9) = xy(x-3)(x+3)
b, x3 +y3 +2x2 -2xy+2y2 = (x^3 + y^3 ) + (2x^2 -2xy+2y^2 )
= (x+y)(x^2-xy+y^2)+2(x^2-xy+y^2)
=(x^2+xy+y^2)(x+y+2)
c, 5x^2 -5xy-9x+9y= 5x(x-y)-9(x-y)=(x-y)(5x-9)
d, m^3 +4m^2 +3m = m( m^2 +4m+3)=m(m^2+m+3m+3)=m(m+1)(m+3)