1/ phân tích các đa thức sau thành nhân tử:
a) x2-5x
b) x2(x+1)-x-1
c) (x-1)3-3x(2-x)
d) 2ab-b2
e) 9x2+6xy+y
f) x3-c2y+y-x
K
Khách
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Những câu hỏi liên quan
1 tháng 11 2023
a: \(x^2-9-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)-x^2\left(x^2-9\right)\)
\(=\left(x^2-9\right)\left(1-x^2\right)\)
\(=\left(1-x\right)\left(1+x\right)\left(x-3\right)\left(x+3\right)\)
b: \(x^2\left(x-y\right)+y^2\left(y-x\right)\)
\(=x^2\left(x-y\right)-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x-y\right)\left(x+y\right)=\left(x-y\right)^2\cdot\left(x+y\right)\)
c: \(x^3+27+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)
\(=\left(x+3\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x+3\right)\)
d: \(x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
e: \(3x^2-4x-4\)
\(=3x^2-6x+2x-4\)
\(=3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x+2\right)\)
g: \(x^4+64y^4\)
\(=x^4+16x^2y^2+64y^4-16x^2y^2\)
\(=\left(x^2+8y^2\right)^2-\left(4xy\right)^2\)
\(=\left(x^2+8y^2-4xy\right)\left(x^2+8y^2+4xy\right)\)
1 tháng 11 2023
h: \(a^2+b^2+2a-2b-2ab\)
\(=a^2-2ab+b^2+2a-2b\)
\(=\left(a-b\right)^2+2\left(a-b\right)=\left(a-b\right)\left(a-b+2\right)\)
i: \(\left(x+1\right)^2-2\left(x+1\right)\left(y-3\right)+\left(y-3\right)^2\)
\(=\left(x+1-y+3\right)^2\)
\(=\left(x-y+4\right)^2\)
k: \(x^2\left(x+1\right)-2x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)^2\)
DN
4
1 tháng 9 2021
\(x^2\left(x+4\right)^2-\left(x+4\right)^2-\left(x^2-1\right)\\ =\left(x+4\right)^2\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^2-1\right)\left[\left(x+4\right)^2-1\right]\\ =\left(x-1\right)\left(x+1\right)\left(x+4-1\right)\left(x+4+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+5\right)\)
KV
9 tháng 12 2023
Bài 3
a) x² + 10x + 25
= x² + 2.x.5 + 5²
= (x + 5)²
b) 8x - 16 - x²
= -(x² - 8x + 16)
= -(x² - 2.x.4 + 4²)
= -(x - 4)²
c) x³ + 3x² + 3x + 1
= x³ + 3.x².1 + 3.x.1² + 1³
= (x + 1)³
d) (x + y)² - 9x²
= (x + y)² - (3x)²
= (x + y - 3x)(x + y + 3x)
= (y - 2x)(4x + y)
e) (x + 5)² - (2x - 1)²
= (x + 5 - 2x + 1)(x + 5 + 2x - 1)
= (6 - x)(3x + 4)
KV
9 tháng 12 2023
Bài 4
a) x² - 9 = 0
x² = 9
x = 3 hoặc x = -3
b) (x - 4)² - 36 = 0
(x - 4 - 6)(x - 4 + 6) = 0
(x - 10)(x + 2) = 0
x - 10 = 0 hoặc x + 2 = 0
*) x - 10 = 0
x = 10
*) x + 2 = 0
x = -2
Vậy x = -2; x = 10
c) x² - 10x = -25
x² - 10x + 25 = 0
(x - 5)² = 0
x - 5 = 0
x = 5
d) x² + 5x + 6 = 0
x² + 2x + 3x + 6 = 0
(x² + 2x) + (3x + 6) = 0
x(x + 2) + 3(x + 2) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 hoặc x + 3 = 0
*) x + 2 = 0
x = -2
*) x + 3 = 0
x = -3
Vậy x = -3; x = -2
18 tháng 10 2021
b: \(8x^2-48x+6xy-36y\)
\(=8x\left(x-6\right)+6y\left(x-6\right)\)
\(=2\left(x-6\right)\left(4x+3y\right)\)
d: \(a^2-2ab+b^2-4\)
\(=\left(a-b\right)^2-4\)
\(=\left(a-b-2\right)\left(a-b+2\right)\)
NN
13 tháng 7 2017
a, x2+2x+1+x+1
=(x2+2x+2)+x
=(x2+2x+12)+x
=(x+1)2+x
=(2x+1)2
=(2x-1).(2x+1 )
NN
14 tháng 7 2017
c,xy-y-2x-2
=(xy-2x)-(y-2)
=x.(y-2)-(y-2)
=(y-2).x
e,xy+xz+y2+yz
=(xy+y2)+(xz+yz)
=y.(x+y)+z.(x+y)
=(x+y).(y+z)
d,x3+x2+x+1
=(x3+x2)+(x+1)
=x2.(x+1)+(x+1)
=x2.(x+1)
b,y2+xy+x+2y+1
=(y2+2y)+(xy+x+1)
=y.(y+2) + x.(y+2)
=(y+2).(y+x)
A
3 tháng 9 2020
a, \(x^2-4x+3=0\Leftrightarrow\left(x-3\right)\left(x-1\right)=0\)
TH1 : x = 3 ; TH2 : x = 1
b, \(2x^2-3x-2=0\Leftrightarrow\left(x-2\right)\left(x+\frac{1}{2}\right)=0\)
TH1 : x = 2 ; TH2 : x = -1/2
c, Đặt \(x^2=t\left(t\ge0\right)\)
\(t^2+2t-8=0\Leftrightarrow\left(t-2\right)\left(t+4\right)=0\)
TH1 : t = 2 ; TH2 : t = -4
Tương tự ...
3 tháng 9 2020
1a)
x2 - 4x + 3 = x2 - x - 3x + 3
= x( x - 1 ) - 3( x - 1 )
= ( x - 1 )( x - 3 )
2c)
2x2 - 3x - 2 = 2x2 + x - 4x - 2
= x( 2x +1 ) - 2( 2x + 1 )
= ( 2x + 1 )( x - 2 )
3e)
x4 + 2x2 - 8 (*)
Đặt t = x2
(*) <=> t2 + 2t - 8
= t2 - 2t + 4t - 8
= t( t - 2 ) + 4( t - 2 )
= ( t - 2 )( t + 4 )
= ( x2 - 2 )( x2 + 4 )
4b) x2 + 4x - 12 = x2 - 2x + 6x - 12
= x( x - 2 ) + 6( x - 2 )
= ( x - 2 )( x + 6 )
d) 2x3 + x - 2x2 - 1 = 2x2( x - 1 ) + 1( x - 1 )
= ( x - 1 )( 2x2 + 1 )
f) x2 - 2xy - 3y2 = ( x2 - 2xy + y2 ) - 4y2
= ( x - y )2 - ( 2y )2
= ( x - y - 2y )( x - y + 2y )
= ( x - 3y )( x + y )
13 tháng 8 2018
1) \(3\left(x+4\right)-x^2-4x=3\left(x+4\right)-x\left(x+4\right)=\left(x+4\right)\left(3-x\right)\)
2) \(5x^2-5y^2-10x+10y=5\left(x^2-y^2\right)-10\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y\right)-10\left(x-y\right)=\left(x-y\right)\left(5x+5y-10\right)\)
3) \(x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right)\)
4) \(ax-bx-a^2+2ab-b^2=x\left(a-b\right)-\left(a^2-2ab+b^2\right)\)
\(=x\left(a-b\right)-\left(a-b\right)^2=\left(a-b\right)\left(x-a+b\right)\)
5) \(x^3-x^2-x+1=x^2\left(x-1\right)-\left(x-1\right)=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x-1\right)\left(x+1\right)=\left(x-1\right)^2\left(x+1\right)\)
6) \(x^2+4x-y^2+4=x^2+4x+4-y^2=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
8 tháng 12 2023
2: \(8xy-24xy+16x\)
\(=8x\cdot y-8x\cdot3y+8x\cdot2\)
\(=8x\left(y-3y+2\right)=8x\left(-2y+2\right)\)
\(=-16y\left(y-1\right)\)
3: \(xy-x=x\cdot y-x\cdot1=x\left(y-1\right)\)
11: \(2mx-4m2xy+6mx\)
\(=2mx-2my\cdot4y+2mx\cdot3\)
\(=2mx\left(1-4y+3\right)\)
\(=2mx\left(4-4y\right)=8mx\left(1-y\right)\)
12: \(7x^2y^5-14x^3y^4-21y^3\)
\(=7y^3\cdot x^2y^2-7y^3\cdot2x^3y-7y^3\cdot3\)
\(=7y^3\left(x^2y^2-2x^3y-3\right)\)
13: \(2\left(x-y\right)-a\left(x-y\right)\)
\(=2\cdot\left(x-y\right)-a\cdot\left(x-y\right)\)
\(=\left(x-y\right)\left(2-a\right)\)
tik cho mk nha
2x2 - 7x +5= 2x2-2x-5x+5=(2x2-2x)-(5x-5)=2x(x-1)-5(x-1)
= (x-1)(2x-5)
ok
a) x^2 - 5x = x .(x-5)
b) x^2 (x+1)-x-1 = x^2(x+1) - (x+1)
= (x+1) . (x^2 - 1)
c) (x-1)^3- 3x(2-x) = x^3 - 3x^2 + 3x + 1 + 3x^2 - 6x
= x^3 - 3x + 1
= x(x^2 - 3 ) + 1
d) 2ab - b^2 = b(2a - b)
e) 9x^2 + 6xy + y = 9x^2 + 6xy + y^2 - y^2 +y
= (3x + y)^2 +y(y - 1)