Question

Đơn giản biểu thức sau:

A= (x+y+z)³- (x+y-z)³- (y+z-x)³- (z+x-y)³

Answer 1

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

    \(\Rightarrow A=\left[\left(x+y\right)^3+3\left(x+y\right)^2z+3\left(x+y\right)z^2+z^3\right]-\left[\left(x+y\right)^3-3\left(x+y\right)^2z+3\left(x+y\right)z^2-z^3\right]-\left[z^3-3z^2\left(x-y\right)+3z\left(x-y\right)^2-\left(x-y\right)^3\right]-\left[z^3+3z^2\left(x-y\right)+3x\left(x-y\right)^2+\left(x-y\right)^3\right]\)

\(\Rightarrow A=6\left(x+y\right)^2z-6z\left(x-y\right)^2\)

\(\Rightarrow A=24xyz\)

_Chúc cậu học tốt_