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6 tháng 9 2020

a) \(\left(x+y\right)^3-x^3-y^3\)

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

\(=\left(x+y\right)\left[\left(x+y\right)^2-x^2+xy-y^2\right]\)

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

\(=3xy\left(x+y\right)\)

b) \(x^2+y^2+2xy+yz+xz\)

\(=\left(x^2+2xy+y^2\right)+\left(yz+xz\right)\)

\(=\left(x+y\right)^2+z\left(x+y\right)\)

\(=\left(x+y\right)\left(x+y+z\right)\)

c) \(x^2-10xy-1+25y^2\)

\(=\left(x^2-10xy+25y^2\right)-1\)

\(=\left(x-5y\right)^2-1\)

\(=\left(x-5y-1\right)\left(x-5y+1\right)\)

d) \(ax^2-ax+bx^2-bx+a+b\)

\(=(ax^2+bx^2)-(ax+bx)+(a+b)\)

\(=x^2(a+b)-x(a+b)+(a+b)\)

\(=(a+b)(x^2-x+1)\)

e)\(x^2-2y+3xz+x-2y+3z\)

\(=(x^2+x)-(2xy+2y)+(3xz+3z)\)

\(=x(x+1)-2y(x-1)+3z(x+1)\)

\(=(x+1)(x-2y+3z)\)

f) \(xyz-xy-yz-xz+x+y+z-1\)

\(=(xyz-xy)-(yz-y)-(xz-x)+(z-1)\)

\(=xy(z-1)-y(z-1)-x(z-1)+(z-1)\)

\(=(z-1)(xy-y-x+1)\)

\(=(z-1)[y(x-1)-(x-1)]\)

\(=(z-1)(x-1)(y-1)\)

_Học tốt_

1: \(=a\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(a-4\right)\)

2: \(=x\left(x+b\right)+a\left(x+b\right)=\left(x+b\right)\left(x+q\right)\)

3: \(=a\left(x+1\right)-b\left(x+1\right)+c\left(x+1\right)\)

\(=\left(x+1\right)\left(a-b+c\right)\)

6: \(=\left(x-y\right)^2-4=\left(x-y-2\right)\left(x-y+2\right)\)

8 tháng 9 2020

A = xy + y - 2x - 2

= y( x + 1 ) - 2( x + 1 )

= ( x + 1 )( y - 2 )

B = x2 - 3x + xy - 3y

= x( x - 3 ) + y( x - 3 )

= ( x - 3 )( x + y )

C = 3x2 - 3xy - 5x + 5y

= 3x( x - y ) - 5( x - y )

= ( x - y )( 3x - 5 )

D = xy + 1 + x + y

= y( x + 1 ) + ( x + 1 )

= ( x + 1 )( y + 1 )

E = ax - bx + ab - x2

= ( ax - x2 ) + ( ab - bx )

= x( a - x ) + b( a - x )

= ( a - x )( x + b )

F = x2 + ab + ax + bx

= ( ax + x2 ) + ( ab + bx )

= x( a + x ) + b( a + x )

= ( a + x )( x + b )

G = a3 - a2x - ay + xy

= a2( a - x ) - y( a - x )

= ( a - x )( a2 - y )

Bonus : = ( a - x )[ a2 - ( √y )2 ]

             = ( a - x )( a - √y )( a + √y )

H = 2xy + 3z + 6y + xz

= ( 6y + 2xy ) + ( 3z + xz )

= 2y( 3 + x ) + z( 3 + x )

= ( 3 + x )( 2y + z )

8 tháng 9 2020

A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1

B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)

C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)

D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)

E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)

F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)

G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)

H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)

b) Ta có: \(x^3-x^2y-xy^2+y^3\)

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

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

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

\(=\left(x+y\right)\left(x-y\right)^2\)

22 tháng 10 2016

a) \(g\left(x,y\right)=x^2-10xy+9y^2=x^2-xy-9xy+9y^2\)

\(=x\left(x-y\right)-9y\left(x-y\right)=\left(x-y\right)\left(x-9y\right)\).

 

22 tháng 10 2016

b )\(f\left(x,y\right)=x^6+x^4+x^2y^2+y^4-y^6\)

\(=x^6-y^6+x^4+x^2y^2+y^4\)

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

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

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

\(=\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\left[\left(x-y\right)\left(x+y\right)+1\right]\)

\(=\left(x^2+xy+y^2\right)\left(x^2-2y+y^2\right)\left(x^2-y^2+1\right)\)

Vậy \(f\left(x,y\right)=\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\left(x^2-y^2+1\right)\)

 

 

 

21 tháng 7 2017

a, \(\left(2x+1\right)^2-2\left(2x+1\right)\left(x-3\right)+\left(x-3\right)^2\)

\(=\left(2x+1-x+3\right)^2=\left(x+4\right)^2\)

b, \(xy+xz+3y+3z=x\left(y+z\right)+3\left(y+z\right)=\left(x+3\right)\left(y+z\right)\)

c, \(xy-xz+y-z=x\left(y-z\right)+\left(y-z\right)=\left(x+1\right)\left(y-z\right)\)

d, \(x^2-xy-8x+8y=\left(x^2-xy\right)-\left(8x-8y\right)\)

\(=x\left(x-y\right)-8\left(x-y\right)=\left(x-8\right)\left(x-y\right)\)

e, \(x^2+2xy+y^2-xz-yz=\left(x^2+2xy+y^2\right)-\left(xz+yz\right)\)

\(=\left(x+y\right)^2-z\left(x+y\right)=\left(x+y+z\right)\left(x+y\right)\)

f, \(25-4x^2-4xy-y^2=25-\left(4x^2+4xy+y^2\right)\)

\(=5^2-\left(2x+y\right)^2=\left(5-2x-y\right)\left(5+2x+y\right)\)

21 tháng 7 2017

1,

a, (2x + 1- x + 3)2 = (x+4)2

b,\(x\left(y+z\right)+3\left(y+z\right)=\left(y+z\right)\left(x+3\right)\)

c, \(x\left(y-z\right)+\left(y-z\right)=\left(y-z\right)\left(x+1\right)\)

d,\(x\left(x-y\right)+8\left(y-x\right)\)=\(\left(x-y\right)\left(x-8\right)\)

e,\(\left(x+y\right)^2-z\left(x+y\right)\)=\(\left(x+y\right)\left(x+y-z\right)\)

f,\(25-\left(4x^2+4xy+y^2\right)=5^2-\left(2x+y\right)^2\)

\(=\left(5+2x+y\right)\left(5-2x-y\right)\)

Chúc các bn hc tốtbanh

Bài 3:

a: =>(2x-7)(x-2)=0

=>x=7/2 hoặc x=2

b: =>(x-1)(x+2)=0

=>x=1 hoặc x=-2

d: =>2x+3=0

hay x=-3/2

20 tháng 10 2021

b: \(x^2-6x+xy-6y\)

\(=x\left(x-6\right)+y\left(x-6\right)\)

\(=\left(x-6\right)\left(x+y\right)\)

c: \(2x^2+2xy-x-y\)

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

\(=\left(x+y\right)\left(2x-1\right)\)

e: \(x^3-3x^2+3x-1=\left(x-1\right)^3\)