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16 tháng 8 2020

a) \(x\left(x-y\right)+x-y\)

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

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

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

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

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

c) \(5x^2-5xy-10x+10y\)

\(=5x\left(x-y\right)-10\left(x-y\right)\)

\(=\left(x-y\right)\left(5x-10\right)\)

d) \(4x^2+8xy-3x-6y\)

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

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

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

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

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

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

2 tháng 1 2018

cái này cách tốt nhất là vào Cốc Cốc Math rồi gõ các nhân tử vào là nó sẽ ra nhé !

^_^

2 tháng 1 2018

\(2x^4-9x^3+2x^3-9x^2+7x^2+7x+6x+6\)

\(\left(2x^4+2x^3\right)-\left(9x^3+9x^2\right)+\left(7x^2+7x\right)+\left(6x+6\right)\)

\(2x^3\left(x+1\right)-9x^2\left(x+1\right)+7x\left(x+1\right)+6\left(x+1\right)\)

\(\left(x+1\right)\left(2x^3-9x^2+7x+6\right)\)

b)\(\left(10x^4-50x^3y\right)+\left(23x^3y-115x^2y^2\right)+\left(5x^2y^2-25xy^3\right)-\left(2xy^3-10y^4\right)\)

\(10x^3\left(x-5y\right)+23x^2y\left(x-5y\right)+5xy^2\left(x-5y\right)-2y^3\left(x-5\right)\)

18 tháng 6 2015

a)5x2y-10xy2

=5xy(x-2y)

b,:4x(2y-z)+7y(z-2y)

=4x(2y-z)-7y(2y-z)

=(2y-z)(4x-7y)

c,:y(x-z)+7(z-x)

=y(x-z)-7(x-z)

=(x-z)(y-7)

d)36-12x+x^2​

=x2-2.x.6+62

=(x-6)2

e) (x-5)^2-16

=(x-5)2-42

=(x-5-4)(x-5+4)

=(x-9)(x-1)

f) ​8x^3+1/27

=(2x)3+(1/3)3

=(2x+1/3)(4x2+2/3.x+1/9)

31 tháng 10 2020

a) \(6x^3-12x^2y^2+6xy^3=6x.\left(x^2-2xy^2+y^3\right)\)

b) \(\left(x^2+4\right)^2-16=\left(x^2+4-4\right)\left(x^2+4+4\right)=x^2\left(x^2+8\right)\)

c) \(5x^2-5xy-10x+10y=\left(5x^2-5xy\right)-\left(10x-10y\right)=5x\left(x-y\right)-10\left(x-y\right)\)

\(=\left(x-y\right)\left(5x-10\right)=5\left(x-y\right)\left(x-2\right)\)

d) \(a^3-3a+3b-b^3=\left(a^3-b^3\right)-\left(3a-3b\right)=\left(a-b\right)\left(a^2+ab+b^2\right)-3.\left(a-b\right)\)

\(=\left(a-b\right)\left(x^2+ab+b^2-3\right)\)

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

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

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

g) \(x^4-5x^2+4=x^4-4x^2+4-x^2=\left(x^4-4x^2+4\right)-x^2=\left(x^2-2\right)^2-x^2\)

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

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

k) \(\left(a^3-27\right)-\left(3-a\right)\left(6a+9\right)=\left(a-3\right).\left(a^2+3a+9\right)+\left(a-3\right)\left(6a+9\right)\)

\(\left(a-3\right)\left(a^2+3a+9+6a+9\right)=\left(a-3\right)\left(a^2+9a+18\right)\)

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

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

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

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

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

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

\(=\left(x-y\right)\left[\left(xy-zx\right)-\left(zy-z^2\right)\right]\)

\(=\left(x-y\right)\left[x\left(y-z\right)-z\left(y-z\right)\right]\)

\(\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

31 tháng 7 2019

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

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

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

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

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

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

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

31 tháng 7 2019

a) \(2x^2-5xy+3y^2\)

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

\(=2x\left(x-y\right)-3y\left(x-y\right)\)

\(=\left(2x-3y\right)\left(x-y\right)\)

7 tháng 10 2019

a,  \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)\(=x^2y+xy^2+y^2z+yz^2+x^2z+xz^2+2xyz\)

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

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

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

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

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

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

b, \(2x^2+2y^2-x^2z+z-y^2z-2\)

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

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

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

27 tháng 7 2017

a) \(x^2+2x+1-y^2 = (x^2 +2x+1) – y^2\)

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

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

b) \(2xy+z+2x+yz\)

\(=\left(2xy+2x\right)+\left(z+yz\right)\)

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

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

c) \(x^2+x-xy-y\)

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

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

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

d) \(5x^2-5xy+10x+10y\)

\(=\left(5x^2-5xy\right)+\left(10x+10y\right)\)

\(=5x\left(x-y\right)-10\left(x-y\right)\)

\(=\left(x-y\right)\left(5x-10\right)\)

27 tháng 7 2017

a, x2+2x+1-y2= (x+1)2-y2= (x+1-y)(x+1+y)
b, 2xy+z+2x+yz= (2xy+2x)+(z+yz)
= 2x(y+1)+z(y+1)
= (2x+z)(y+1)
c, x2 +x - xy - y = x(x+1) - y(x+1)
= (x - y)(x+1)
d, 5x2 - 5xy - 10x + 10y=5x(x-y) - 10(x-y)
= (5x-10)(x-y).(Câu này có thể là sai đề nên mik đã sửa lại đề cho dễ làm nha). Chúc bạn học tốt!!!

18 tháng 8 2020

a)

\(=x^2\left(2x+3\right)+\left(2x+3\right)\)

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

b)

\(=a\left(a-b\right)+a-b\)

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

c)

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

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

d)

\(=x^3\left(x-2\right)+10x\left(x-2\right)\)

\(=x\left(x^2+10\right)\left(x-2\right)\)

e)

\(=x\left(x^2+2x+1\right)\)

\(=x\left(x+1\right)^2\)

f)

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

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

18 tháng 8 2020

a,2x3+3x2+2x+3

=(2x3+2x)+(3x2+3)

=2x(x2+1)+3(x2+1)

=(x2+1)(2x+3)

b,a2-ab+a-b

=(a2-ab)+(a-b)

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

=(a-b)(a+1)

c,2x2+4x+2-2y2

=2(x2+2x+1-y2)

=2[(x2+2x+1)-y2 ]

=2[(x+1)2-y2 ]

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

d,x4-2x3+10x2-20x

=(x4-2x3)+(10x2-20x)

=x3(x-2)+10x(x-2)

=(x-2)(x3+10x)

=(x-2)[x(x2+10)]

e,x3+2x2+x

=x(x2+2x+1)

=x(x+1)2

f,xy+y2-x-y

=(xy+y2)-(x-y)

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

=(x+y)(y-1)