phân tích đa thức thành nhân tử bằng phương pháp đặt nhân tử chung : 1) (x-1)¹-(x²-1)+(x³-1)
2) (x²-16)+(4-x)
3) (2x-5)² -2x+5
4) (x³-27)-2(x²-9)
5) (x-2)(x²-2x+7)+2(x-2)(x+1)-3(2-x)
6) (x²-9)+(3-x)(x²+x)
7) x²-4x+(3x-12)3
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14 tháng 10 2020
16) 2x + 2y - x2 - xy = ( 2x + 2y ) - ( x2 + xy ) = 2( x + y ) - x( x + y ) = ( x + y )( 2 - x )
17) x2 - 2x - 4y2 - 4y = ( x2 - 4y2 ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2( x + 2y ) = ( x + 2y )( x - 2y - 2 )
18) x2y - x3 - 9y + 9x = ( x2y - x3 ) - ( 9y - 9x ) = x2( y - x ) - 9( y - x ) = ( y - x )( x2 - 9 ) = ( y - x )( x - 3 )( x + 3 )
19) x2( x - 1 ) + 16( 1 - x ) = x2( x - 1 ) - 16( x - 1 ) = ( x - 1 )( x2 - 16 ) = ( x - 1 )( x - 4 )( x + 4 )
20) 2x2 + 3x - 2xy - 3y = ( 2x2 - 2xy ) + ( 3x - 3y ) = 2x( x - y ) + 3( x - y ) = ( x - y )( 2x + 3 )
A
14 tháng 10 2020
20, \(2x^2+3x-2xy-3y=2x\left(x-y\right)+3\left(x-y\right)=\left(2x+3\right)\left(x-y\right)\)
16, \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
17, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x-2y-2\right)\left(x+2y\right)\)
18, \(x^2y-x^3-9y+9x=-x\left(x^2-9\right)+y\left(x^2-9\right)=\left(-x-y\right)\left(x^2-9\right)=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
19, \(x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x^2-16\right)\left(x-1\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)
14 tháng 10 2020
6) \(9x^3y^2+3x^2y^2=3x^2y^2\left(3x+1\right)\)
7) \(x^3+2x^2+3x=x\left(x^2+2x+3\right)\)
8) \(6x^2y+4xy^2+2xy=2xy\left(3x+2y+1\right)\)
9) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=5x\left(x-2y\right)\left(x-3\right)\)
10) \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(3+5x\right)\)
14 tháng 10 2020
6) 9x3y2 + 3x2y2 = 3x2y2( 3x + 1 )
7) x3 + 2x2 + 3x = x( x2 + 2x + 3 )
8) 6x2y + 4xy2 + 2xy = 2xy( 3x + 2y + 1 )
9) 5x2( x - 2y ) - 15x( x - 2y ) = 5x( x - 2y )( x - 3 )
10 3( x - y ) - 5x( y - x ) = 3( x - y ) + 5x( x - y ) = ( x - y )( 3 + 5x )
12 tháng 3 2022
8: \(=\left(x-2y\right)\cdot x\cdot\left(x+3\right)\)
9: \(=\left(5x+2\right)\left(x-3\right)-x\left(x-3\right)\)
\(=\left(x-3\right)\left(4x+2\right)\)
=2(2x+1)(x-3)
3: \(=2\left(x+2\right)\left(25x-15-x\right)\)
\(=2\left(x+2\right)\left(24x-15\right)\)
=6(x+2)(8x-5)
25 tháng 9 2021
a) \(\left(x+1\right)\left(x+2\right)\left(x+4\right)\left(x+5\right)-4=\left(x^2+6x+5\right)\left(x^2+6x+8\right)-4\)
Đặt \(t=x^2+6x+5\)
\(PT=t\left(t+3\right)-4=t^2+3t-4=\left(t-1\right)\left(t+4\right)\)
Thay t: \(PT=\left(x^2+6x+5-1\right)\left(x^2+6x+5+4\right)=\left(x^2+6x+4\right)\left(x^2+6x+9\right)=\left(x^2+6x+4\right)\left(x+3\right)^2\)
b) Đặt \(t=\left(2x+1\right)^2\)
\(PT=t^2-3t+2=\left(t^2-3t+\dfrac{9}{4}\right)-\dfrac{1}{4}=\left(t+\dfrac{3}{2}\right)^2-\dfrac{1}{4}=\left(t+1\right)\left(t+2\right)\)
Thay t:
\(PT=\left[\left(2x+1\right)^2+1\right]\left[\left(2x+1\right)^2+2\right]=\left[4x^2+4x+2\right]\left[4x^2+4x+3\right]=2\left[2x^2+2x+1\right]\left[4x^2+4x+3\right]\)
4 tháng 12 2023
1: \(x\left(x-1\right)+\left(1+x\right)^2\)
\(=x^2-x+x^2+2x+1\)
\(=2x^2+x+1\)
Đa thức này ko phân tích được nha bạn
2: \(\left(x+1\right)^2-3\left(x+1\right)\)
\(=\left(x+1\right)\cdot\left(x+1\right)-\left(x+1\right)\cdot3\)
\(=\left(x+1\right)\left(x+1-3\right)\)
\(=\left(x+1\right)\left(x-2\right)\)
3: \(2x\cdot\left(x-2\right)-\left(x-2\right)^2\)
\(=2x\left(x-2\right)-\left(x-2\right)\cdot\left(x-2\right)\)
\(=\left(x-2\right)\left(2x-x+2\right)\)
\(=\left(x-2\right)\left(x+2\right)\)
4: \(3x\left(x-1\right)^2-\left(1-x\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^2\cdot\left(x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(3x+x-1\right)\)
\(=\left(x-1\right)^2\cdot\left(4x-1\right)\)
5: \(3x\left(x+2\right)-5\left(x+2\right)^2\)
\(=\left(x+2\right)\cdot3x-\left(x+2\right)\cdot\left(5x+10\right)\)
\(=\left(x+2\right)\left(3x-5x-10\right)\)
\(=\left(-2x-10\right)\left(x+2\right)\)
\(=-2\left(x+5\right)\left(x+2\right)\)
6: \(4x\left(x-y\right)+3\left(y-x\right)^2\)
\(=4x\left(x-y\right)+3\left(x-y\right)^2\)
\(=\left(x-y\right)\cdot4x+\left(x-y\right)\left(3x-3y\right)\)
\(=\left(x-y\right)\cdot\left(4x+3x-3y\right)\)
\(=\left(x-y\right)\left(7x-3y\right)\)
14 tháng 10 2020
11) \(3x\left(x-1\right)+5\left(1-x\right)=\left(3x-5\right)\left(x-1\right)\)
12) \(2\left(2x-1\right)+3\left(1-2x\right)=1-2x\)
13) \(10x\left(x-y\right)-8y\left(y-x\right)=2\left(x-y\right)\left(5x+4y\right)\)
14) \(3x\left(y+2\right)-3\left(y+2\right)=3\left(x-1\right)\left(y+2\right)\)
15) \(x^2-y^2-2x+2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right)\)
9 tháng 9 2023
1) \(x\left(x-1\right)+\left(1-x\right)^2\)
\(=x\left(x-1\right)+\left(x-1\right)^2\)
\(=\left(x-1\right)\left(x+x-1\right)\)
\(=\left(x-1\right)\left(2x-1\right)\)
2) \(2x\left(x-2\right)-\left(x-2\right)^2\)
\(=\left(x-2\right)\left[2x-\left(x-2\right)\right]\)
\(=\left(x-2\right)\left(2x-x+2\right)\)
\(=\left(x-2\right)\left(x+2\right)\)
3) \(3x\left(x-1\right)^2-\left(1-x\right)^3\)
\(=3x\left(x-1\right)^2+\left(x-1\right)^3\)
\(=\left(x-1\right)^2\left(3x+x-1\right)\)
\(=\left(x-1\right)^2\left(4x-1\right)\)
4) \(3x\left(x+2\right)-5\left(x+2\right)^2\)
\(=\left(x+2\right)\left[3x-5\left(x+2\right)\right]\)
\(=\left(x+2\right)\left(3x-5x-10\right)\)
\(=\left(x+2\right)\left(-2x-10\right)\)
\(=-2\left(x+2\right)\left(x+5\right)\)
