(√с-7√d)*(c+7√cd+49d)-(√c+7√d)*(c-7√cd+49d)

(√с-7√d)*(c+7√cd+49d) = (√с)^3 - (7√d)^3 (√c+7√d)*(c-7√cd+49d) = (√с)^3 + (7√d)^3 (√с)^3 - (7√d)^3 - (√с)^3 - (7√d)^3 = -2(7√d)^3 = -686d√d Ответ: -686d√d

[latex](\sqrt{c}-7\sqrt{d})\cdot(c+7\sqrt{cd}+49d)-(\sqrt{c}+7\sqrt{d})\cdot(c-7\sqrt{cd}+49d)=(c\cdot\sqrt{c}+7\sqrt{cd}\cdot\sqrt{c}+49d\cdot\sqrt{c}-c\cdot7\sqrt{d}-7\sqrt{d}\cdot7\sqrt{cd}-7\sqrt{d}\cdot49d)-(c\cdot\sqrt{c}-7\sqrt{cd}\cdot\sqrt{c}+49d\cdot\sqrt{c}+c\cdot7\sqrt{d}-7\sqrt{d}\cdot7\sqrt{cd}+7\sqrt{d}\cdot49d)=[/latex] [latex]\\(c\sqrt{c}+7\sqrt{c^{2}d}+49d\sqrt{c}-7c\sqrt{d}-49\sqrt{cd^{2}}-343d\sqrt{d})-(c\sqrt{c}-7\sqrt{c^{2}d}+49d\sqrt{c}+7c\sqrt{d}-49\sqrt{cd^{2}}+343d\sqrt{d})=(c\sqrt{c}+7c\sqrt{d}+49d\sqrt{c}-7c\sqrt{d}-49d\sqrt{c}-343d\sqrt{d})-(c\sqrt{c}-7c\sqrt{d}+49d\sqrt{c}+7c\sqrt{d}-49d\sqrt{c}+343d\sqrt{d})=[/latex] [latex]\\c\sqrt{c}+7c\sqrt{d}+49d\sqrt{c}-7c\sqrt{d}-49d\sqrt{c}-343d\sqrt{d}-c\sqrt{c}+7c\sqrt{d}-49d\sqrt{c}-7c\sqrt{d}+49d\sqrt{c}-343d\sqrt{d}=(c\sqrt{c}-c\sqrt{c})+(7c\sqrt{d}-7c\sqrt{d}+7c\sqrt{d}-7c\sqrt{d})+(49d\sqrt{c}-49d\sqrt{c}-49d\sqrt{c}+49d\sqrt{c})+(-343d\sqrt{d}-343d\sqrt{d})=-686d\sqrt{d}[/latex]