Phân tích đa thức thành nhân tử:
- x^35+x^34+x^33+...x^2+x+1
- x^m+1-X^m-x+1 (m thuộc N*)
- x^2-6xy+9y^2-9
- (x-9)(x-7)+1
K
Khách
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TT
2
Những câu hỏi liên quan
NH
Phân tích các đa thức thành nhân tử:
a. x6-y6
b.x35+x34+x33+.......+x2+x+1
c.x2-6xy+9y2-9
e.(x-9)(x-7)+1
2
3 tháng 7 2017
Ta có : x35 + x34 + x33 +.......+ x2 + x + 1
= (x35 + x34 ) + (x33 + x32) +.......+ (x3 + x2) + (x + 1)
= x34(x + 1) + x32(x + 1) + .... + x2(x + 1) + (x + 1)
= (x + 1) ( x34 + x32 + ..... + x2 + 1)
3 tháng 7 2017
Ta có : (x - 9)(x - 7) + 1
= x2 - 16x + 63 + 1
= x2 - 16x + 64
= x2 - 2.x.8 + 82
= (x - 8)2
NT
3 tháng 7 2017
a.x\(^6\)-y\(^6\)=(x\(^2\))\(^3\)+(y\(^2\))\(^3\) =(x\(^2\)+y\(^2\))(x\(^4\)-x\(^2\)y\(^2\)+y\(^4\))
b.x\(^{35}\)+x\(^{34}\)+......+x+1 =x\(^{34}\).(x+1)+......+(x+1)
=(x\(^{34}\)+x\(^{32}\)+......+x\(^2\)+1)(x+1)
c.x\(^2\)-6xy+9y\(^2\)-9 =x\(^2\)-2.3xy+(3y)\(^2\)-3\(^2\) =(x-3y)\(^2\)-3\(^2\)
=(x-3y-3)(x-3y+3)
d.(x-9)(x-7)+1 =x\(^2\)-7x-9x+63+1 =x\(^2\)-16x+64
=x\(^2\)-2.8x+8\(^2\) =(x-8)\(^2\)
30 tháng 7 2021
m, \(x^2+4x+4-4y^2=\left(x+2\right)^2-\left(2y\right)^2=\left(x+2-2y\right)\left(x+2+2y\right)\)
n, \(x^2+6xy+9y^2-4z^2=\left(x+3y\right)^2-\left(2z\right)^2=\left(x+3y-2z\right)\left(x+3y+2z\right)\)
PN
2
31 tháng 12 2021
a) \(4\left(x+y\right)\)
b) \(\left(x-3y\right)^2\)
c) \(x^3-x-x^2+1=x\left(x^2-1\right)-\left(x^2-1\right)=\left(x^2-1\right)\left(x-1\right)=\left(x-1\right)\left(x+1\right)\left(x-1\right)\)
31 tháng 12 2021
a) \(4 (x + y)\)
b) \((x - 3y)^2\)
c) \(x^3 - x - x^2 + 1 = x (x^2 - 1) - (x^2 - 1) = (x^2 - 1) (x - 1) = (x - 1) (x + 1) (x - 1)\)
T
28 tháng 8 2023
1) \(3x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(x-1\right)\left(3x+5\right)\)
2) \(4x(x-2y)-8y(2y-x)\)
\(=4x\left(x-2y\right)+8y\left(x-2y\right)\)
\(=\left(4x+8y\right)\left(x-2y\right)\)
\(=4\left(x+2y\right)\left(x-2y\right)\)
3) \(a^2\left(x-1\right)+b^2\left(1-x\right)\)
\(=a^2\left(x-1\right)-b^2\left(x-1\right)\)
\(=\left(a^2-b^2\right)\left(x-1\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(x-1\right)\)
4) \(3x\left(x-a\right)+4a\left(a-x\right)\)
\(=3x\left(x-a\right)-4a\left(x-a\right)\)
\(=\left(x-a\right)\left(3x-4a\right)\)
5) \(5x\left(x-y\right)^2+10y^2\left(y-x\right)^2\)
\(=5x\left(x-y\right)^2+10y^2\left(x-y\right)^2\)
\(=\left(5x+10y^2\right)\left(x-y\right)^2\)
\(=5\left(x+2y^2\right)\left(x-y\right)^2\)
6) \(3x\left(x-3\right)^2+9\left(3-x\right)^2\)
\(=3x\left(x-3\right)^2+9\left(x-3\right)^2\)
\(=\left(3x+9\right)\left(x-3\right)^2\)
\(=3\left(x+3\right)\left(x-3\right)^2\)
7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)
\(=x\left(a-m\right)^2-y\left(a-m\right)^2\)
\(=\left(x-y\right)\left(a-m\right)^2\)
8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)
\(=6y^2\left(x-1\right)^2+9y\left(x-1\right)^2\)
\(=\left(6y^2+9x\right)\left(x-1\right)^2\)
\(=3\left(2y^2+3x\right)\left(x-1\right)^2\)
#Ayumu
2 tháng 1 2023
a: =(x^2-x+1)(x^2+x+1)
b: =x^2-6xy+9y^2=(x-3y)^2
c: =5x(x^2-2xy+y^2)
=5x(x-y)^2
d: =(x-3)^2
e: =(2y-z)(4x+7y)
2 tháng 1 2023
a)HĐT:(x^2+1-x)(x^2+1+x)
b)=x^2-2.x.3y+(3y)^2
c)=5x(x^2-2xy+y^2)
=5x(x-y)^2
d)x^2-2.3.x+3^2
=(x-3)^2
e)(2y-z)+7y(2y-z)
=(2y-z)(1+7y)
C
1
1 tháng 11 2020
M = x9 - x7 + x6 - x5 - x4 + x3 - x2 + 1
= ( x9 - x7 ) + ( x6 - x4 ) - ( x5 - x3 ) - ( x2 - 1 )
= x7( x2 - 1 ) + x4( x2 - 1 ) - x3( x2 - 1 ) - ( x2 - 1 )
= ( x2 - 1 )( x7 + x4 - x3 - 1 )
= ( x - 1 )( x + 1 )[ x4( x3 + 1 ) - ( x3 + 1 ) ]
= ( x - 1 )( x + 1 )( x3 + 1 )( x4 - 1 )
= ( x - 1 )( x + 1 )( x + 1 )( x2 - x + 1 )( x2 - 1 )( x2 + 1 )
= ( x + 1 )2( x - 1 )( x2 - x + 1 )( x - 1 )( x + 1 )( x2 + 1 )
= ( x + 1 )3( x - 1 )2( x2 + 1 )( x2 - x + 1 )
Ta có : x35 + x34 + .... + x2 + x + 1
= (x35 + x34) + .... + (x3 + x2) + (x + 1)
= x34(x + 1) + ..... + x2(x + 1) + 1(x + 1)
= (x + 1) (x34 + x32 + .... + x2 + 1)
Ta có : (x - 9)(x - 7) + 1
= x2 - 16x + 63 + 1
= x2 - 16x + 64
= (x - 8)2