\(x-y=2\Rightarrow\left(x-y\right)^2=4\Leftrightarrow x^2-2xy+y^2=4\Rightarrow x^2+y^2=4+2.xy=100\)Ta có:

\(x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)=2.\left(100+48\right)=296\)

\(A=9\)

\(a,\left(x+2\right)^2-9=0\)

\(\Leftrightarrow\left(x+2-3\right)\left(x+2+3\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+5\right)=0\Rightarrow\left[{}\begin{matrix}x-1=0\\x+5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\)\(b,\left(x-2\right)^2-x^2+4=0\)

\(\Leftrightarrow x^2-4x+4-x^2+4=0\)

\(\Leftrightarrow-4x+8=0\Leftrightarrow-4x=-8\Rightarrow x=2\)

\(a,\left(x+2\right)^2-9=0\)

\(\Leftrightarrow\left(x+2\right)^2-3^2=0\)

\(\Leftrightarrow\left(x+2-3\right)\left(x+2+3\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+5\right)=0\Rightarrow\left[{}\begin{matrix}x-1=0\\x-5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=5\end{matrix}\right.\)\(b,\left(x-2\right)^2-x^2+4=0\)

\(\Leftrightarrow x^2-4x+4-x^2+4=0\)

\(\Leftrightarrow-4x+8=0\Leftrightarrow-4x=-8\Rightarrow x=2\)

\(a,\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\) \(=x^3+1-x^3+1=2\)

\(b,x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)

\(=x\left(x^2-16\right)-\left(x^4-1\right)=x^3-16x-x^4+1\) \(c,\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2\)

\(=x^2-9-x^2-2x-1=-2x-10\)

\(d,\left(4x-3\right)\left(4x+3\right)-16x^2\)

\(=16x^2-9-16x^2=-9\)

\(e,\left(x+4\right)\left(x^2-4x+16\right)-x^3=x^3+64-x^3=64\)

58,

\(\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{x+1}{x\left(x+1\right)}-\dfrac{x}{x\left(x+1\right)}=\dfrac{x+1-x}{x\left(x+1\right)}=\dfrac{1}{x\left(x+1\right)}\)b,

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{n\left(n+1\right)}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{n}-\dfrac{1}{n+1}\)\(=1-\dfrac{1}{n\left(n+1\right)}=\dfrac{n^2+n-1}{n\left(n+1\right)}\)

\(B=\dfrac{1}{\left(x^2+9x+20\right)}+\dfrac{1}{x^2+11x+30}+\dfrac{1}{x^2+13x+42}\)\(=\dfrac{1}{\left(x^2+4x\right)+\left(5x+20\right)}+\dfrac{1}{\left(x^2+5x\right)+\left(6x+30\right)}+\dfrac{1}{\left(x^2+6x\right)+\left(7x+42\right)}\)\(=\dfrac{1}{x\left(x+4\right)+5\left(x+4\right)}+\dfrac{1}{x\left(x+5\right)+6\left(x+5\right)}+\dfrac{1}{x\left(x+6\right)+7\left(x+6\right)}\)\(=\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{\left(x+5\right)\left(x+6\right)}+\dfrac{1}{\left(x+6\right)\left(x+7\right)}\)\(=\dfrac{1}{x+4}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+6}+\dfrac{1}{x+6}-\dfrac{1}{x-7}\)\(=\dfrac{1}{x+4}-\dfrac{1}{x+7}\)