a)
\(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3+3xy\left(x+y\right)+z^3-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2+\left(x+y\right)z+z^2\right]+3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+2xy+y^2-yz-zx+z^2-3xy\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
\(x^3+y^3+z^3-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xyz\left(x+y+z\right)\)\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
xy(x+y)+yz(y+z)+xz(x+z)+2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(y + x)
= (x + y)(xy + zx + zy + z²)
= (x + y)[x(y + z) + z(y + z)]
= (x + y)(y + z)(z + x)
Mấy bài này làm dài lắm
bn đăng từng bài ik
b)
\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(x+z\right)\)
\(=xy\left(x+y\right)+\left[yz\left(y+z\right)+xyz\right]+\left[zx\left(z+x\right)+x+y+z\right]\)
\(=xy\left(x+y\right)+yz\left(x+y+z\right)+zx\left(x+y+z\right)\)
\(=xy\left(x+y\right)+z\left(x+y+z\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(xy+z\left(x+y+z\right)\right)\)
\(=\left(x+y\right)\left(xy+zx+xy+z^2\right)\)
\(=\left(x+y\right)\left[\left(xy+zx\right)+\left(zy+z^2\right)\right]\)
\(=\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)
\(=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)
c)
\(x\left(x+y\right)-5x-5y\)
\(=x\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x-5\right)\left(x+y\right)\)