Question

C/m đẳng thức:

(xy + z)\(^2\) - x\(^2\)y\(^2\)= z(2xy+z)

Answer 1

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

\(=\left(xy\right)^2+2xyz+z^2-\left(xy\right)^2\)

\(=2xyz+z^2\)

\(=z\left(2xy+z\right)\left(đpcm\right)\)

Answer 2

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

\(=x^2y^2+2xyz+z^2-x^2y^2=z^2+2xyz\)

\(=z\left(2xy+z\right)=VP\Rightarrow dpcm\)