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26 tháng 8 2019

1, 5a2xy-10a3x-15ay = 5a( axy - 2a\(^2\)x - 3y )

2, mxy-m2x+my = m( xy - mx + y )

3, 2mx-4m2xy+6mx = 2mx( 1 - 2my + 3 ) = 2mx( 4 - 2my )

4, a2b-2ab2+ab = ab( a - 2b + 1 )

5, 5a2b-2ab2+ab = ab( 5a - 2b +1 )

6, -3x2y3-6x3y2-x2y2 = -3x\(^2\)y\(^2\) ( y + 2x + 1 )

7, 5x2y4-10x4y2+5x2y2 = 5x\(^{^2y^2}\)( y\(^2\) - 2x\(^2\) + 1 )

8, -2x3y4-4x4y3+2x3y3 = 2\(x^3y^3\) ( -y - 2x + 1 )

9, 4x3y2-8x3y+16xy2-24 = 4( x\(^3\)y\(^2\) - 2x\(^3\)y + 4 xy\(^2\) - 6 )

10, 12x3y-6xy+3x = 3x( 4x\(^2\)y - 2y + 1 )

11, 2(x-y)-a(x-y) = ( 2 - a ) ( x - y )

12, a(x-y)+b(x-y)= ( a + b ) ( x - y )

13, m(x+y)-n(x+y) = ( m - n ) ( x + y )

14, 2a(x+y)-4(x+y) = ( 2a - 4 )( x + y ) = 2( a - 2 ) ( x + y )

15, 3a(x+y)-6ab(x+y) = ( 3a - 6ab )( x + y ) = 3a( 1 - 2b ) ( x + y )

16, 5a2(x-y)+10a(x-y) = ( 5a\(^2\)+10a )( x - y ) = 5a( a + 2 ) ( x - y )

17, -2ab(x-y)-4a(x-y) = ( -2ab - 4a )( x - y ) = -2a( b + 2 )( x - y )

18, 3a(x-y)+2(x-y) = ( 3a + 2 ) ( x - y )

19, m(a-b)-m2(a-b) = ( m - m\(^2\) ) ( a - b ) = m( 1 - m ) ( a - b )

20, mx(a+b)-m(a+b) = ( mx - m ) ( a + b ) = m( x - 1 )( a + b )

21, x(a-b)-y(b-a) = x( a - b ) + y( a - b ) = ( x + y ) ( a - b )

22, ab(x-5)-a2(5-x) = ab( x - 5 ) + a\(^2\)( x - 5 ) = ( ab + a\(^2\) ) ( x - 5 ) = a( b + a )( x - 5 )

23, 2a2(x-y)-4a(y-x)= 2a\(^2\)( x - y ) + 4a( x - y )=( 2a\(^2\) + 4a ) ( x - y )= 2a( a + 2 )( x - y )

26 tháng 8 2019

Đăng ít thôi =))

a. \(5a^2xy-10a^3x-15ay=5a\left(axy-2a^2x-3y\right)\)

b. \(mxy-m^2x+my=m\left(xy-mx+y\right)\)

c. \(2mx-4m^2xy+6mx=2mx\left(1-2my+3\right)=2mx\left(-2my+4\right)\)

d. \(a^2b-2ab^2+ab=ab\left(a-2b+1\right)\)

e. \(5a^2b-2ab^2+ab=ab\left(5a-2b+1\right)\)

g.

30 tháng 5 2018

b) 8a3 + 4a2b - 2ab2 – b3 = (8a3 – b3 ) + (4a2b - 2ab2 )

= (2a – b)(4a2 + 2ab + b2) + 2ab(2a – b)

= (2a – b)( 4a2 + 2ab + b2 + 2ab) = (2a – b)(2a + b)2

11: \(\dfrac{1}{3}x^2y^2\left(6x+\dfrac{2}{3}x^2-y\right)\)

\(=2x^3y^2+\dfrac{2}{9}x^4y^2-\dfrac{1}{3}x^2y^3\)

12: \(\dfrac{3}{4}x^3y^2\left(4x^2y-x+y^5\right)\)

\(=3x^5y^3-\dfrac{3}{4}x^4y^2+\dfrac{3}{4}x^3y^7\)

13: \(-5x^2y^4\left(3x^2y^3-2x^3y^2-xy\right)\)

\(=-15x^4y^7+10x^5y^6+5x^3y^5\)

7 tháng 8 2019

20 tháng 8 2023

a, 4\(x^3\).y + \(\dfrac{1}{2}\)yz

  =y.(4\(x^3\) + \(\dfrac{1}{2}\)z)

b, (a2 + b2 - 5)2 - 2.(ab + 2)2

 = [a2 + b2 - 5  - \(\sqrt{2}\)(ab + 2) ].[ a2 + b2 - 5 + \(\sqrt{2}\)(ab +2)]

20 tháng 8 2023

a) \(4x^3y+\dfrac{1}{2}yz=y\left(4x^3+\dfrac{1}{2}z\right)\)

b) \(\left(a^2+b^2-5\right)^2-2.\left(ab+2\right)^2\)

\(=\left[\left(a^2+b^2-5\right)+2\left(ab+2\right)\right]\left[\left(a^2+b^2-5\right)-2\left(ab+2\right)\right]\)

\(=\left[a^2+b^2-5+2ab+4\right]\left[a^2+b^2-5-2ab-4\right]\)

\(=\left[a^2+b^2+2ab-1\right]\left[a^2+b^2-2ab-9\right]\)

\(=\left[\left(a+b\right)^2-1\right]\left[\left(a-b\right)^2-9\right]\)

\(=\left[\left(a+b+1\right)\left(a+b-1\right)\right]\left[\left(a-b+3\right)\left(a-b-3\right)\right]\)

31 tháng 7 2021

1. x2 - 6x + 9=(x-3)2

2. 25 +  10x + x2=(x+5)2

3. \(\dfrac{1}{4}a^2+2ab^2+4b^4=\left(\dfrac{1}{2}a+2b^2\right)^2\)

4.\(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}-y^4\right)^2\)

5.x+ 8y3=(x+8y)(x2-8xy+64y2)

6.8y3 -125=(2y-5)(4y2+10y+25)

7.a6-b3=(a2-b)(a4+a2b+b2)

8 x2 - 10x + 25=(x-2)2

1) \(x^2-6x+9=\left(x-3\right)^2\)

2) \(25+10x+x^2=\left(5+x\right)^2\)

3) \(\dfrac{1}{4}a^2+2ab+4b^4=\left(\dfrac{1}{2}a+2b^2\right)^2\)

4) \(\dfrac{1}{9}-\dfrac{2}{3}y^4+y^8=\left(\dfrac{1}{3}-y^4\right)^2\)

5) \(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)

6) \(8y^3-125=\left(2y-5\right)\left(4y^2+10y+25\right)\)

7) \(a^6-b^3=\left(a^2-b\right)\left(a^4+a^2b+b^2\right)\)

8) \(x^2-10x+25=\left(x-5\right)^2\)

9) \(8x^3-\dfrac{1}{8}=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)

 

4 tháng 10 2020

a,\(2axy-4a^2xy^2+6a^3x^2\)

\(=2ax\left(y-2ay^2+3a^2x\right)\)

b,\(5a^2xy-10a^3x-15ay\)

\(=5a\left(axy-2ax-3y\right)\)

Tự lm tiếp, tất cả đều dùng bằng phương phép đặt nhân tử chung nhé

4 tháng 10 2020

23) \(2axy-4a^2xy^2+6a^3x^2\)

\(=2ax\left(y-2ay^2+3a^2x\right)\)

24) \(5a^2xy-10a^3x-15ay\)

\(=5a\left(axy-2a^2x-3y\right)\)

25) \(mxy-m^2x+my\)

\(=m\left(xy-mx+y\right)\)

26) \(2mx-4m^2xy+6mx\)

\(=2mx\left(1-2my+3\right)\)

\(=4mx\left(2-my\right)\)

21 tháng 8 2021

\(a^2+2ab^2+4b^2=\left(a+2b^2\right)^2\)

21 tháng 8 2021

(a+2b2)2 ct: a2+2ab+b2=(a+b)2

\(4x^3y-16xy^2=4xy\left(x^2-4y^2\right)=4xy\left(x-2y\right)\left(x+2y\right)\)

3 tháng 10 2021

phân tích đa thức sau thành nhân tử 
x3-x+3x2y+3xy2+y3-y
giúp câu này nữa nha

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: \(2\left(x-y\right)-a\left(x-y\right)\)

\(=2\cdot\left(x-y\right)-a\cdot\left(x-y\right)\)

\(=\left(x-y\right)\left(2-a\right)\)