نویسنده : امیر انصاری

1. $$
   (-3 \sqrt{2x}) (4 \sqrt{6}) , x \ge 0
   $$
   
2. $$
   7 \sqrt{3} (5 \sqrt{5} - 6 \sqrt{3})
   $$
   
3. $$
   (8 \sqrt{2} - 5) (9 \sqrt{5} + 6 \sqrt{10})
   $$
   
4. $$
   9 \sqrt[3]{2w} (\sqrt[3]{4w} + 7 \sqrt[3]{28}) , w \ge 0
   $$
   

پاسخ

1. $$
   (-3 \sqrt{2x}) (4 \sqrt{6}) , x \ge 0 \\
   = -3(4) \sqrt{(2x)(6)}\\
   =-12 \sqrt{(2x)(2)(3)}\\
   = -12 (2) \sqrt{3x}\\
   = -24 \sqrt{3x}
   $$
   
2. $$
   7 \sqrt{3} (5 \sqrt{5} - 6 \sqrt{3})\\
   = 7 \sqrt{3} (5 \sqrt{5}) - 7 \sqrt{3} (6\sqrt{3})\\
   = 35 \sqrt{15} - 42 \sqrt{9}\\
   = 35 \sqrt{15} - 42 (3)\\
   = 35 \sqrt{15} - 126
   $$
   
3. $$
   (8 \sqrt{2} - 5) (9 \sqrt{5} + 6 \sqrt{10})\\
   = 8 \sqrt{2} (9 \sqrt{5}) + 8 \sqrt{2} (6 \sqrt{10}) - 5 (9 \sqrt{5}) - 5 (6 \sqrt{10})\\
   = 72 \sqrt{10} + 48 \sqrt{20} - 45 \sqrt{5} - 30 \sqrt{10} \\
   = 72 \sqrt{10} + 48 \sqrt{(4)(5)} - 45 \sqrt{5} - 30 \sqrt{10}\\
   = 72 \sqrt{10} + 96 \sqrt{5} - 45 \sqrt{5} - 30 \sqrt{10} \\
   = 42 \sqrt{10} + 51 \sqrt{5}
   $$
   
4. $$
   9 \sqrt[3]{2w} (\sqrt[3]{4w} + 7 \sqrt[3]{28}) , w \ge 0\\
   = 9 \sqrt[3]{2w (4w)} + 63 \sqrt[3]{2w (28)} \\
   = 9 \sqrt[3]{8w^2} + 63 \sqrt[3]{56w}\\
   = 18 \sqrt[3]{w^2} + 126 \sqrt[3]{7w}
   $$
   

حالا نوبت شماست

1. $$
   5 \sqrt{3} (\sqrt{6})
   $$
   
2. $$
   -2 \sqrt[3]{11} (4 \sqrt[3]{2} - 3 \sqrt[3]{3})
   $$
   
3. $$
   (4 \sqrt{2} + 3) (\sqrt{7} - 5 \sqrt{14})
   $$
   
4. $$
   -2 \sqrt{11c} (4 \sqrt{2c^3} - 3 \sqrt{3}), c \ge 0
   $$