bài 1:

a)

\(x+1=\left(x+1\right)^2\\ \Leftrightarrow\left(x+1\right)^2-\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)x=0\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=0\end{matrix}\right.\)

b)\(x^3+x=0\\ \Leftrightarrow x\left(x^2+1\right)=0\\ \Rightarrow x=0\)

c)\(x^2-10x=-25\\ \Leftrightarrow x^2-2.5.x+25=0\\ \Leftrightarrow\left(x-5\right)^2=0\\ \Rightarrow x=5\)

bài 2:

a)

\(x^6-y^6=\left(x^3+y^3\right)\left(x^3-y^3\right)\\ =\left(x+y\right)\left(x^2+y^2+xy\right)\left(x-y\right)\left(x^2+y^2-xy\right)\)

b)

\(x^3+y^3+z^3-3xyz=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\\ =\left(x+y+z\right)^3-3z\left(x+y\right)\left(x+y+z\right)-3xy\left(x+y\right)-3xzy\\ =\left(x+y+z\right)^3-\left(3xz+3zy\right)\left(x+y+z\right)-3xy\left(x+y+z\right)\\ =\left(x+y+z\right)\left(x^2+y^2+z^2+2xy+2xz+2zy-3xz-3zy-3xy\right)\\ =\left(x+y+z\right)\left(x^2+y^2+z^2-xy-zx-zy\right)\)