=(32−102+32)252+92−102=(−42)242=(42)242=42__{\displaystyle {\begin{matrix}&=&\displaystyle {\frac {\left(3{\sqrt {2}}-10{\sqrt {2}}+3{\sqrt {2}}\right)^{2}}{5{\sqrt {2}}+9{\sqrt {2}}-10{\sqrt {2}}}}\\&=&\displaystyle {\frac {\left(-4{\sqrt {2}}\right)^{2}}{4{\sqrt {2}}}}\\&=&\displaystyle {\frac {\left(4{\sqrt {2}}\right)^{2}}{4{\sqrt {2}}}}\\&=&{\underline {\underline {4{\sqrt {2}}}}}\end{matrix}}}
={(x2+x+1)(x2−x+1)}(x4−x2+1)(x8−x4+1)={(x4+2x2+1)−x2}(x4−x2+1)(x8−x4+1)=(x4+x2+1)(x4−x2+1)(x8−x4+1)=(x8+x4+1)(x8−x4+1)=x16+x8+1__{\displaystyle {\begin{matrix}&=&\left\{\left(x^{2}+x+1\right)\left(x^{2}-x+1\right)\right\}\left(x^{4}-x^{2}+1\right)\left(x^{8}-x^{4}+1\right)\\&=&\left\{\left(x^{4}+2x^{2}+1\right)-x^{2}\right\}\left(x^{4}-x^{2}+1\right)\left(x^{8}-x^{4}+1\right)\\&=&\left(x^{4}+x^{2}+1\right)\left(x^{4}-x^{2}+1\right)\left(x^{8}-x^{4}+1\right)\\&=&\left(x^{8}+x^{4}+1\right)\left(x^{8}-x^{4}+1\right)\\&=&{\underline {\underline {x^{16}+x^{8}+1}}}\end{matrix}}}
左から掛けていくと、次々に和と差の積の公式が使える形が表れていくのがポイントである。