Cho ( x 2 + y 2 − 17 ) 2 − 4 ( x y − 4 ) 2 = ( x + y + 5 ) ( x − y + 3 ) ( x + y + m ) . ( x − y + n )

Ta có
$\left({{{x}^{2}{+}{y}^{2}{-}{17}}}\right){2}{-}{4}\left({{{x}{y}{-}{4}}}\right){2}$
${=}\left({{{x}^{2}{+}{y}^{2}{-}{17}}}\right){2}{-}\left[{{{2}\left({{{x}{y}{-}{4}}}\right)}}\right]{2}$
${=}\left({{{x}^{2}{+}{y}^{2}{-}{17}{+}{2}{x}{y}{-}{8}}}\right)\left({{{x}^{2}{+}{y}^{2}{-}{17}{-}{2}{x}{y}{+}{8}}}\right)$
${=}\left({{{x}^{2}{+}{y}^{2}{+}{2}{x}{y}{-}{25}}}\right)\left({{{x}^{2}{+}{y}^{2}{-}{2}{x}{y}{-}{9}}}\right)$
${=}\left[{{\left({{{x}{+}{y}}}\right){2}{-}{5}^{2}}}\right]\left[{{\left({{{x}{-}{y}}}\right){2}{-}{3}^{2}}}\right]$
${=}\left({{{x}{+}{y}{+}{5}}}\right)\left({{{x}{+}{y}{-}{5}}}\right)\left({{{x}{-}{y}{+}{3}}}\right)\left({{{x}{-}{y}{-}{3}}}\right)$
$\Rightarrow$ ${m}{=}{-}{5}{;}{n}{=}{-}{3}{ }$
$\Rightarrow$ ${m}{.}{n}{=}\left({{{-}{5}}}\right){.}\left({{{-}{3}}}\right){=}{15}$
Đáp án cần chọn là: D