Question

Giúp mk nhé m.n

(x+y+z)^3-x^3-y^3-z^3

mơn nhìu

Answer 1

Ta có

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

\(\Rightarrow\left(x+y+z\right)^3-x^3-y^3-z^3=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3\)

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

   \(=x^3+y^3+3xy\left(x+y\right)+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)

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

   \(=3\left(x+y\right)\left[x\left(y+x\right)+z\left(y+z\right)\right]\)

\(=3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)