.

a.\(\left(x^2-y^2-z^2\right)=\left(x-y\right)^2-2z\left(x-y\right)+z^2=x^2-2xy+y^2-2zx+2zy+z^2\)

b.\(\left(x+y-z\right)^2=\left(x+y\right)^2-2z\left(x+y\right)+z^2=x^2+2xy+y^2-2zy-2zx+z^2\)

a, b, nhân vào là ra à

c, nghe cứ là lạ

d, cũng nhân là ra hà

\(=x^5-x^4y+x^3y^2-x^2y^3+xy^4+x^4y-x^3y^2+x^2y^3-xy^4+y^5=x^5+y^5\)

a) Ta có: \(VT=\left(x-y-z\right)^2\)

\(=\left(x-y-z\right)\left(x-y-z\right)\)

\(=x^2-xy-xz-yx+y^2+yz-zx+zy+z^2\)

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

=VP(đpcm)

b) Ta có: \(VT=\left(x+y-z\right)^2\)

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

\(=x^2+xy-xz+yx+y^2-yz-zx-zy+z^2\)

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

=VP(đpcm)

c) Sửa đề: Chứng minh \(\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)=x^4-y^4\)

Ta có: \(VT=\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)\)

\(=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4\)

\(=x^4-y^4\)

=VP(đpcm)

d) Ta có: \(VT=\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)\)

\(=x^5-x^4y+x^3y^2-x^2y^3+xy^4+x^4y-x^3y^2+x^2y^3-xy^4+y^5\)

\(=x^5+y^5\)

=VP(đpcm)

Đáp án D

a) Ta có: \(VP=x^2+y^2+z^2-2xy+2yz-2zx\)

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

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

\(=x\left(x-y-z\right)-y\left(x-y-z\right)-z\left(x-y-z\right)\)

\(=\left(x-y-z\right)\left(x-y-z\right)\)

\(=\left(x-y-z\right)^2=VT\)(đpcm)

b) Ta có: \(VP=x^2+y^2+z^2+2xy-2yz-2zx\)

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

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

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

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

\(=\left(x+y-z\right)^2=VT\)(đpcm)

c) Ta có: \(VP=x^4-y^4\)

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

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

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

d) Ta có: \(VT=\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)\)

\(=x^5-x^4y+x^3y^2-x^2y^3+xy^4+x^4y-x^3y^2+x^2y^3-xy^4+y^5\)

\(=x^5+y^5=VP\)(đpcm)

a)biến đổi vế trái ta đc:x(y+z)-y(x-z)=xy+xz-xy+yz

                                                        =(xz+yz)+(xy-xy)

                                                        =z(x+y)=vế phải(đpcm)

b)biến đổi vế trái ta đc:x(y-z)-x(y+a)=xy-xz-xy-xa

                                                         =(xy-xy)-(xz+xa)

                                                         =-(xz+xa)

                                                         =-x(z+a)=vế phải(đpcm)  

a;\(x\left(y+z\right)-y\left(x-z\right)=\left(x+y\right)z\)

\(xy+xz-xy+yz=\left(x+y\right)z\)

\(xz+yz=\left(x+y\right)z\)

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

b;\(x\left(y-z\right)-x\left(y+a\right)=-x\left(z+a\right)\)

\(xy-xz-xy-xa=-x\left(z+a\right)\)

\(-xz-xa=-x\left(z+a\right)\)

\(-x\left(z+a\right)=-x\left(z+a\right)\left(ĐPCM\right)\)

P/S: sai thì thôi nha 

đây là dạng bài chứng minh cho hai vế đẳng thức bằng nhau ,bạn Phương ngay từ đầu đã cho nó bằng nhau rồi thì cần gì phải chứng minh nữa

\(\Rightarrow\left(x+y+z\right)^2\ge\left(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\right)^2\ge3\left(\dfrac{1}{xy}+\dfrac{1}{yz}+\dfrac{1}{xz}\right)=\dfrac{3\left(x+y+z\right)}{xyz}\Rightarrow x+y+z\ge\dfrac{3}{xyz}\)

\(x+y+z=\dfrac{x+y+z}{3}+\dfrac{2\left(x+y+z\right)}{3}\ge\dfrac{1}{3}\left(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\right)+\dfrac{2}{3}.\dfrac{3}{xyz}\ge\dfrac{1}{3}\left(\dfrac{9}{x+y+z}\right)+\dfrac{2}{xyz}=\dfrac{3}{x+y+z}+\dfrac{2}{xyz}\left(đpcm\right)\)

\(dấu"="xảy\) \(ra\Leftrightarrow x=y=z=1\)