$\displaystyle \begin{array}{{>{\displaystyle}l}} 1) 89^{2} +11^{2} +22.89\ \\ =89^{2} +2.11.89+11^{2}\\ =( 89+11)^{2} =100^{2} =10000\\ 2) 100^{2} -99^{2} +98^{2} -97^{2} +...+2^{2} -1\ \\ ( 100-99)( 100+99) +( 98-97)( 98+97) +..+( 2-1)( 2+1)\\ =100+99+98+97+...+2+1\ \\ =\frac{( 1+100) .100}{2} =5050\\ 3)( 2+1)\left( 2^{2} +1\right)\left( 2^{3} +1\right)\left( 2^{4} +1\right)\left( 2^{8} +1\right)\left( 2^{16} +1\right) -2^{32}\\ =( 2-1)( 2+1)\left( 2^{2} +1\right)\left( 2^{3} +1\right)\left( 2^{4} +1\right)\left( 2^{8} +1\right)\left( 2^{16} +1\right) -2^{32}\\ =\left( 2^{2} -1\right)\left( 2^{2} +1\right)\left( 2^{3} +1\right)\left( 2^{4} +1\right)\left( 2^{8} +1\right)\left( 2^{16} +1\right) -2^{32}\\ =\left( 2^{4} -1\right)\left( 2^{4} +1\right)\left( 2^{8} +1\right)\left( 2^{16} +1\right)\left( 2^{3} +1\right) -2^{32}\\ =\left( 2^{8} -1\right)\left( 2^{8} +1\right)\left( 2^{16} +1\right)\left( 2^{3} +1\right) -2^{32}\\ =\left( 2^{16} -1\right)\left( 2^{16} +1\right)\left( 2^{3} +1\right) -2^{32}\\ =\left( 2^{32} -1\right) 9-2^{32}\\ =2^{32} .9-9-2^{32} =8^{32} -9 \end{array}$