画像に示された数式を計算する問題です。具体的には、以下の2つの問題があります。 * **問題2:** * (1) $(2\sqrt{2}+1)(\sqrt{2}-2)$ * (2) $(\sqrt{5}+2)(\sqrt{5}+1)$ * (3) $(\sqrt{3}+\sqrt{2})^2$ * (4) $(2\sqrt{2}-1)^2$ * (5) $(\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2})$ * **問題3:** * (1) $(\sqrt{2}+1)(\sqrt{2}-1)+\sqrt{2}(\sqrt{2}-1)$ * (2) $(\sqrt{6}+\sqrt{3})^2-(\sqrt{6}-\sqrt{3})^2$

1. 問題の内容

画像に示された数式を計算する問題です。具体的には、以下の2つの問題があります。

* **問題2:**

* (1) $(2\sqrt{2}+1)(\sqrt{2}-2)$

* (2) $(\sqrt{5}+2)(\sqrt{5}+1)$

* (3) $(\sqrt{3}+\sqrt{2})^2$

* (4) $(2\sqrt{2}-1)^2$

* (5) $(\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2})$

* **問題3:**

* (1) $(\sqrt{2}+1)(\sqrt{2}-1)+\sqrt{2}(\sqrt{2}-1)$

* (2) $(\sqrt{6}+\sqrt{3})^2-(\sqrt{6}-\sqrt{3})^2$

2. 解き方の手順

各問題について、以下の手順で計算します。

* **問題2:**

* (1) $(2\sqrt{2}+1)(\sqrt{2}-2) = 2\sqrt{2}\sqrt{2} - 4\sqrt{2} + \sqrt{2} - 2 = 4 - 3\sqrt{2} - 2 = 2 - 3\sqrt{2}$

* (2) $(\sqrt{5}+2)(\sqrt{5}+1) = \sqrt{5}\sqrt{5} + \sqrt{5} + 2\sqrt{5} + 2 = 5 + 3\sqrt{5} + 2 = 7 + 3\sqrt{5}$

* (3) $(\sqrt{3}+\sqrt{2})^2 = (\sqrt{3})^2 + 2\sqrt{3}\sqrt{2} + (\sqrt{2})^2 = 3 + 2\sqrt{6} + 2 = 5 + 2\sqrt{6}$

* (4) $(2\sqrt{2}-1)^2 = (2\sqrt{2})^2 - 2(2\sqrt{2})(1) + 1^2 = 4(2) - 4\sqrt{2} + 1 = 8 - 4\sqrt{2} + 1 = 9 - 4\sqrt{2}$

* (5) $(\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2}) = (\sqrt{7})^2 - (\sqrt{2})^2 = 7 - 2 = 5$

* **問題3:**

* (1) $(\sqrt{2}+1)(\sqrt{2}-1)+\sqrt{2}(\sqrt{2}-1) = (\sqrt{2})^2 - 1^2 + \sqrt{2}\sqrt{2} - \sqrt{2} = 2 - 1 + 2 - \sqrt{2} = 3 - \sqrt{2}$

* (2) $(\sqrt{6}+\sqrt{3})^2-(\sqrt{6}-\sqrt{3})^2 = (6 + 2\sqrt{18} + 3) - (6 - 2\sqrt{18} + 3) = 9 + 2\sqrt{9 \cdot 2} - (9 - 2\sqrt{9 \cdot 2}) = 9 + 6\sqrt{2} - 9 + 6\sqrt{2} = 12\sqrt{2}$

3. 最終的な答え

* **問題2:**

* (1) $2 - 3\sqrt{2}$

* (2) $7 + 3\sqrt{5}$

* (3) $5 + 2\sqrt{6}$

* (4) $9 - 4\sqrt{2}$

* (5) $5$

* **問題3:**

* (1) $3 - \sqrt{2}$

* (2) $12\sqrt{2}$