phân tích đa thức sau thành nhân tử
\(x^2-2xy+y^2-6x+6y\)
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TP
3
30 tháng 8 2021
b, 2xy+2xyz
=2xy(1+z)
d,27x^2+6x^2
=3x2(9+2)
=3x2.11
f, (3x-6y)x+y(x-2y)
=3(x-2y)+y(x-2y)
=(3+y)(x-2y)
23 tháng 9 2017
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
19 tháng 10 2021
\(=x\left(x-6\right)+y\left(x-6\right)=\left(x+y\right)\left(x-6\right)\)
VL
1
NT
5
5 tháng 7 2021
a) \(6x-6y=6\left(x-y\right)\)
b)\(2xy+3x+6y+xz\)
\(=\left(2xy+xz\right)+\left(6y+3z\right)\)
\(=x\left(2y+z\right)+3\left(2y+z\right)\)
\(=\left(2y+z\right)\left(x+3\right)\)
c)\(x^2+6x+9-y^2\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x-y+3\right)\left(x+y+3\right)\)
d) \(9x-x^3\)
\(=x\left(9-x^2\right)\)
\(=x\left(3-x\right)\left(3+x\right)\)
e)\(x^2-xy+x-y\)
\(=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
5 tháng 7 2021
a, 6x - 6y = 6( x-y )
b, 2xy + 3z + 6y + xz
= ( 2xy + 6y ) + ( 3z + xz )
= 2y( x + 3 ) + z ( 3 + x )
= 2y( 3 + x ) + z ( 3 + x )
= ( 3 + x ) ( 2y + z )
c, x2 + 6x + 9 - y2 = ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x + 3 - y ) ( x + 3 + y )
d , 9x - x3 = x ( 9 - x2 )
= x ( 3 - x ) ( 3 + x )
e, x2 - xy + x - y =( x 2 - xy ) + ( x - y )
= x ( x - y ) + ( x - y )
= ( x - y ) ( x + 1 )
H
2
T
17 tháng 9 2018
a)\(x^2+2xy-6y-9=x^2-9+2y.\left(x-3\right)=\left(x-3\right)\left(x+3\right)+2y.\left(x-3\right)\)
\(=\left(x-3\right).\left(x+3+2y\right)\)
b) \(x^3+x^2-6x=x^3-6x+9+x^2-9\)
\(=x^3+3x^2-3x^2-9x+3x+9+\left(x-3\right)\left(x+3\right)\)
\(=x^2.\left(x+3\right)-3x.\left(x+3\right)+3.\left(x+3\right)+\left(x-3\right).\left(x+3\right)\)
\(=\left(x+3\right).\left(x^2-3x+3+x-3\right)\)
\(=\left(x+3\right).\left(x^2-2x\right)=x.\left(x+3\right).\left(x-2\right)\)
LC
17 tháng 9 2018
a, \(x^2+2xy-6y-9\)
\(=\left(x^2+2xy+y^2\right)-\left(y^2+6y+9\right)\)
\(=\left(x+y\right)^2-\left(y-3\right)^2\)
\(=\left(x+2y-3\right)\left(x+3\right)\)
b, \(x^3+x^2-6x\)\(=x\left(x^2+3x-2x-6\right)\)
\(=x\left(x+3\right)\left(x-2\right)\)
18 tháng 11 2021
a)\(=3x\left(x+2y\right)\)
c)\(=\left(x-7\right)\left(x-1\right)\)
b)\(=x\left(x-2y\right)+3\left(x-2y\right)=\left(x+3\right)\left(x-2y\right)\)
d)\(=\left(2x\right)^2-y^2=\left(2x-y\right)\left(2x+y\right)\)
18 tháng 11 2021
\(a,3x^2+6xy=3x\left(x+2y\right)\\ c,x^2-8x+7=\left(x^2-x\right)-\left(7x-7\right)=x\left(x-1\right)-7\left(x-1\right)=\left(x-1\right)\left(x-7\right)\\ b,x^2-2xy+3x-6y=\left(x^2+3x\right)-\left(2xy+6y\right)=x\left(x+3\right)-2y\left(x+3\right)=\left(x+3\right)\left(x-2y\right)\\ d,4x^2-y^2=\left(2x-y\right)\left(2x+y\right)\)
x\(^2\)-2xy+y\(^2\)-6x+6y
=(x-y)\(^2\)-6(x+y)
=-6(x+y)+(x-y)\(^2\)
\(x^2-2xy+y^2-6x+6y=\left(x-y\right)^2-6\left(x-y\right)=\left(x-y\right)\left(x-y-6\right)\)