Question

1) (3√5-2)(3√5+2)2) (√2+1)²3) (1-√3)²​

Answer 1

Ответ:

1. 41
2. 3
3. -2

Объяснение:

1. а^2-b^2 = (a-b) (a+b)

2. возводим во 2 степень и складываем (2+1=3)

3. возводим во 2 степень и вычитаем (1-3=-2)

Answer 2

Let's simplify each of the expressions:

1. $(3\sqrt{5}-2)(3\sqrt{5}+2)$

This expression can be simplified using the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$. In this case, $a = 3\sqrt{5}$ and $b = 2$.

Using the formula, we have:

$(3\sqrt{5})^2 - 2^2 = 9 \cdot 5 - 4 = 45 - 4 = 41$

Therefore, $(3\sqrt{5}-2)(3\sqrt{5}+2) = 41$.

2. $(\sqrt{2}+1)^2$

Expanding the square, we have:

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

Using the distributive property, we can multiply each term:

$(\sqrt{2}+1)(\sqrt{2}+1) = \sqrt{2} \cdot \sqrt{2} + \sqrt{2} \cdot 1 + 1 \cdot \sqrt{2} + 1 \cdot 1$

Simplifying, we get:

$2 + 2\sqrt{2} + 1 = 3 + 2\sqrt{2}$

Therefore, $(\sqrt{2}+1)^2 = 3 + 2\sqrt{2}$.

3. $(1-\sqrt{3})^2$

Expanding the square, we have:

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

Using the distributive property, we can multiply each term:

$(1-\sqrt{3})(1-\sqrt{3}) = 1 \cdot 1 + 1 \cdot (-\sqrt{3}) + (-\sqrt{3}) \cdot 1 + (-\sqrt{3}) \cdot (-\sqrt{3})$