العبارة a
\[a = 2\sqrt{2}(4 - \sqrt{2})\]
خطوات الحل
\[= 2\sqrt{2} \cdot 4 - 2\sqrt{2} \cdot \sqrt{2}\]
\[= 8\sqrt{2} - 2 \cdot 2\]
\[= 8\sqrt{2} - 4\]
العبارة b
\[b = \sqrt{3}(\sqrt{3} - 1)\]
خطوات الحل
\[= \sqrt{3} \cdot \sqrt{3} - \sqrt{3}\]
\[= 3 - \sqrt{3}\]
العبارة c
\[c = 5(\sqrt{2} - 2)\]
خطوات الحل
\[= 5\sqrt{2} - 10\]
العبارة d
\[d = -2(5\sqrt{3} - \sqrt{2})\]
خطوات الحل
\[= -10\sqrt{3} + 2\sqrt{2}\]
العبارة e
\[e = 3(2\sqrt{5} - 4)\]
خطوات الحل
\[= 6\sqrt{5} - 12\]
العبارة f
\[f = \sqrt{2}(4\sqrt{2} - 3) - \sqrt{3}(2\sqrt{3} + 1)\]
خطوات الحل
\[= (4 \cdot 2 - 3\sqrt{2}) - (2 \cdot 3 + \sqrt{3})\]
\[= 8 - 3\sqrt{2} - 6 - \sqrt{3}\]
\[= 2 - 3\sqrt{2} - \sqrt{3}\]
العبارة g
\[g = 2\sqrt{3}(4\sqrt{3} - 1) - 4(\sqrt{3} + 2) + 3\sqrt{3}(1 - \sqrt{3})\]
خطوات الحل
\[= (8 \cdot 3 - 2\sqrt{3}) - (4\sqrt{3} + 8) + (3\sqrt{3} - 3 \cdot 3)\]
\[= 24 - 2\sqrt{3} - 4\sqrt{3} - 8 + 3\sqrt{3} - 9\]
\[= (24 - 8 - 9) + (-2\sqrt{3} - 4\sqrt{3} + 3\sqrt{3})\]
\[= 7 - 3\sqrt{3}\]
العبارة h
\[h = 3(2\sqrt{2} - 3) - \sqrt{2}(4 - \sqrt{2}) + 5\sqrt{3}(4 - \sqrt{3})\]
خطوات الحل
\[= (6\sqrt{2} - 9) - (4\sqrt{2} - 2) + (20\sqrt{3} - 15)\]
\[= 6\sqrt{2} - 9 - 4\sqrt{2} + 2 + 20\sqrt{3} - 15\]
\[= (6\sqrt{2} - 4\sqrt{2}) + 20\sqrt{3} + (-9 + 2 - 15)\]
\[= 2\sqrt{2} + 20\sqrt{3} - 22\]
العبارة i
\[i = 2(\sqrt{5} - 1) - 3(4\sqrt{5} - 3)\]
خطوات الحل
\[= 2\sqrt{5} - 2 - 12\sqrt{5} + 9\]
\[= -10\sqrt{5} + 7\]
العبارة k
\[k = (\sqrt{3} - 1)(2 - \sqrt{3})\]
خطوات الحل
\[= 2\sqrt{3} - (\sqrt{3})^2 - 2 + \sqrt{3}\]
\[= 2\sqrt{3} - 3 - 2 + \sqrt{3}\]
\[= 3\sqrt{3} - 5\]
العبارة l
\[l = (\sqrt{2} - 2)(\sqrt{2} + 3)\]
خطوات الحل
\[= (\sqrt{2})^2 + 3\sqrt{2} - 2\sqrt{2} - 6\]
\[= 2 + \sqrt{2} - 6\]
\[= \sqrt{2} - 4\]
العبارة m
\[m = (2\sqrt{3} - 1)(3\sqrt{3} + 4)\]
خطوات الحل
\[= (2\sqrt{3})(3\sqrt{3}) + 8\sqrt{3} - 3\sqrt{3} - 4\]
\[= 18 + 5\sqrt{3} - 4\]
\[= 14 + 5\sqrt{3}\]
العبارة n
\[n = (4 + \sqrt{3})(2\sqrt{3} - 1) + (3\sqrt{2} - 4)(\sqrt{2} - 1)\]
خطوات الحل
\[= (8\sqrt{3} - 4 + 6 - \sqrt{3}) + (6 - 3\sqrt{2} - 4\sqrt{2} + 4)\]
\[= (7\sqrt{3} + 2) + (10 - 7\sqrt{2})\]
\[= 7\sqrt{3} - 7\sqrt{2} + 12\]
العبارة p
\[p = (2\sqrt{5} + 2)(3 - 2\sqrt{5}) - (3\sqrt{3} - 2)(3 - 4\sqrt{3})\]
خطوات الحل
\[= (6\sqrt{5} - 20 + 6 - 4\sqrt{5}) - (9\sqrt{3} - 36 - 6 + 8\sqrt{3})\]
\[= (2\sqrt{5} - 14) - (17\sqrt{3} - 42)\]
\[= 2\sqrt{5} - 14 - 17\sqrt{3} + 42\]
\[= 2\sqrt{5} - 17\sqrt{3} + 28\]