Question

Thu gọn biểu thức :

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

2, \(\left(2x+y\right)^2-4x\cdot\left(2x+y\right)+4x^2\)

3, \(\left(x+y\right)^2-2\cdot\left(x^2-y^2\right)+\left(x-y\right)^2\)

Answer 1

1) \(\left(x-y-z\right)^2-\left(y+z\right)^2=\left(x\right).\left(x-2y-2z\right)=x^2-2yx-2zx\) 2) \(\left(2x+y\right)^2-4x\left(2x+y\right)+4x^2\Leftrightarrow\left(2x+y\right)\left(2x+y-4x\right)+4x^2\)

\(=\left(2x+y\right)\left(y-2x\right)+4x^2=\left(y^2-4x^2\right)+4x^2=y^2-4x^2+4x^2=y^2\)

3) \(\left(x+y\right)^2-2\left(x^2-y^2\right)+\left(x-y\right)^2\)

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

\(=4y^2=\left(2y\right)^2\)