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2 tháng 7 2021
a) xy(x + y) + yz(y + z) + xz(z + x) + 3xyz
= xy(X + y + z) + yz(x + y + z) + xz(X + y + z)
= (x + y +z)(xy + yz+ xz)
b) xy(x + y) - yz(y + z) - xz(z - x)
= x2y + xy2 - y2z - yz2 - xz2 + x2z
= x2(y + z) - yz(y + z) + x(y2 - z2)
= x2(y + z) - yz(y + z) + x(y + z)(y - z)
= (y + z)(x2 - yz + xy - xz)
= (y + z)[x(x + y) - z(x + y)]
= (y + z)(x + y)(x - z)
c) x(y2 - z2) + y(z2 - x2) + z(x2 - y2)
= x(y - z)(y + z) + yz2 - yx2 + x2z - y2z
= x(y - z)(y + z) - yz(y - z) - x2(y - z)
= (y - z)((xy + xz - yz - x2)
= (y - z)[x(y - x) - z(y - x)]
= (y - z)(x - z)(y -x)
10 tháng 10 2018
\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+xz\left(x+z\right)\)
\(=xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+z\right)\)
\(=y\left(x+y+z\right)\left(x+z\right)+xz\left(x+z\right)\)
\(=\left(x+z\right)\left(x^2+y^2+yz+xz\right)\)
\(=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)
10 tháng 10 2018
\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz.\)
\(=x^2y+xy^2+x^2z+xz^2+2xyz+yz\left(y+z\right)\)
\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z\right)\)
\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+z\right)+y\left(x+z\right)\right]=\left(y+z\right)\left(x+y\right)\left(x+z\right)\)
15 tháng 11 2019
\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)2xyz\)
\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+xz\left(x+z\right)\)
\(=xy\left(x+y+z\right)+yz\left(x+y+z\right)+xz\left(x+z\right)\)
\(=\left(xy+yz\right)\left(x+y+z\right)+xz\left(x+z\right)\)
\(=y\left(x+z\right)\left(x+y+z\right)+xz\left(x+z\right)\)
\(=\left(x+z\right)\left[y\left(x+y+z\right)+xz\right]=\left(x+z\right)\left(xy+y^2+yz+xz\right)\)
\(=\left(x+z\right)\left[y\left(x+y\right)+z\left(x+y\right)\right]\)
\(=\left(x+z\right)\left(z+y\right)\left(y+x\right)\)
\(=\left(x+y\right)\left(y+z\right)\left(z+x\right).\)
Phức tạp. Cs cách nào nhanh kkk?
ko làm đc
why?????