نشر وتبسيط العبارات (تمرين 29)

حل تمرين 29

(أ) $(\sqrt{5} + \sqrt{3})^2$ = $5 + 2\sqrt{15} + 3$ = $8 + 2\sqrt{15}$

(ب) $(\sqrt{7} + \sqrt{3})^2$ = $7 + 2\sqrt{21} + 3$ = $10 + 2\sqrt{21}$

(ج) $(\sqrt{25} - 4)(\sqrt{25} + 4)$ = $25 - 16$ = 9

(د) $(2\sqrt{3} + 3\sqrt{2})^2 - 5(6 + \sqrt{6})$ = $4\cdot3 + 12\sqrt{6} + 9\cdot2 - 30 - 5\sqrt{6}$

= $12 + 12\sqrt{6} + 18 - 30 - 5\sqrt{6}$ = $0 + 7\sqrt{6}$ = 7\sqrt{6}