Phân tích đa thức thành nhân tử bằng phương pháp nhóm hạng tử

a) xy + xz + y

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DT
5 tháng 8 2022

\(\left(a\right):=x\left(y+z\right)+y\left(y+z\right)=\left(y+z\right)\left(x+y\right)\\ \left(b\right):=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\\ \left(c\right):=4^2-\left(x+y\right)^2=\left(4+x+y\right)\left(4-x-y\right)\\ \left(d\right):=x\left(x+y+z\right)-\left(x+y+z\right)=\left(x+y+z\right)\left(x-1\right)\)

24 tháng 7 2016

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

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

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

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

 x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz 
=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2 
=xy(x+y+z)+zx(x+y+z)+yz(y+z) 
=x(y+z)(x+y+z)+yz(y+z) 
=(y+z)(x^2+xy+zx+yz) 
=(x+y)(y+z)(z+x)

t i c k mk nha!!! 565464556756768768787669789789776575656767676945645645654

25 tháng 8 2017

b) \(5x-5y+ax-ay \)

\(=\left(5x-5y\right)+\left(ax-ay\right)\)

\(=5.\left(x-y\right)+a.\left(x-y\right)\)

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

c) \(a^3-a^2x-ay+xy\)

\(=\left(a^3-a^2x\right)-\left(ay-xy\right)\)

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

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

10 tháng 7 2018

a) xy – 3x + 2y – 6

= (xy - 3x) + (2y - 6)

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

= (y - 3)(x + 2)

b) x2y + 4xy + 4y – y3

= y(x2 + 4x + 4 - y2)

= y[(x2 + 4x + 4) - y2]

= y[(x + 2)2 - y2]

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

c) x2 + y2 + xz + yz + 2xy

= (x2 + 2xy + y2) + (xz + yz)

= (x + y)2 + z(x + y)

= (x + y)(x + y + z)

d) x3 + 3x2 – 3x – 1

= (x3 - 1) + (3x2 - 3x)

= (x - 1)(x2 + x + z) + 3x(x - 1)

= (x - 1)(x2 + 4x + 1)

10 tháng 7 2018

a ) 

\(xy-3x+2y-6\)

\(=\left(xy+2y\right)-3x-6\)

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

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

b ) 

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

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

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

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

c ) 

\(x^2+y^2+xz+yz+2xy\)

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

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

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, \(2x^2+2y^2-x^2z+z-y^2z-2\)

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

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

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

19 tháng 8 2020

Bài làm:

a) \(x^2-2xy+y^2-zx+yz\)

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

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

19 tháng 8 2020

a/ \(x^2-2xy+y^2-zx+yz.\)

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

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

c/ \(x^2-y^2-2x-2y.\)

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

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

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

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

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

11 tháng 8 2018

Vụ này khoai à nha !

11 tháng 8 2018

\(b,9x^2+90x+225-\left(x-y\right)^2\)

\(=\left(3x+15\right)^2-\left(x-y\right)^2\)

\(=\left(3x+15-x+y\right)\left(3x+15+x-y\right)\)

\(=\left(2x+y+15\right)\left(4x-y+15\right)\)