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Bao Cao Su
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Pham Van Hung
20 tháng 10 2018 lúc 16:48

     

       \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

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

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

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

kim thanh 2k8
19 tháng 10 2019 lúc 19:40

nick ko hay rồi tcn còn ko hay nữa

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Kaori Miyazono
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Dương Lam Hàng
26 tháng 8 2018 lúc 15:29

a) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

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

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

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

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

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

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

b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

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

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

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

P/s: Sai sót xin bỏ qua.

Nguyễn Trường Giang
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❤  Hoa ❤
20 tháng 10 2018 lúc 17:03

\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz.\)

\(=x^2.\left(y+z\right)+yz.\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)

\(=\left(y+z\right).\left(x^2+yz\right)+x\left(y^{^2}+z^2+2yz\right)\)

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

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

An
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Nguyễn Thị Vân Anh
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ShadowHp
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Nguyễn Quang Đức
8 tháng 3 2020 lúc 9:15

Ta có: \(x^2y-xy^2+y^2z-yz^2+xz^2-x^2z=xy\left(x-y\right)-z\left(x^2-y^2\right)+z^2\left(x-y\right)\)

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

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

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Long Le
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Aeris
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Đinh quang hiệp
22 tháng 6 2018 lúc 21:34

b  \(x^8y^8+x^4y^4+1=x^8y^8+2x^4y^4+1-x^4y^4=\left(x^4y^4\right)^2+2x^4y^4+1-\left(x^2y^2\right)^2\)

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

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

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

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

a  \(3xyz+x\left(y^2+z^2\right)+y\left(x^2+z^2\right)+z\left(x^2+y^2\right)=3xyz+xy^2+xz^2+x^2y+yz^2+x^2z+y^2z\)

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

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

jhfdvbjj
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❤  Hoa ❤
13 tháng 12 2018 lúc 20:51

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

\(=x^2\left(y+z\right)+yz\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)

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

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

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

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

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

❤  Hoa ❤
13 tháng 12 2018 lúc 20:56

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

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

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

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

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

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