Question

6.6
score: 15/17 15/17 answered
question 16
multiply.
\\((2 - \sqrt{5})^2 =\\)

Explanation:

Step1: Apply square of difference formula

Recall $(a-b)^2 = a^2 - 2ab + b^2$, let $a=2$, $b=\sqrt{5}$.
$$(2-\sqrt{5})^2 = 2^2 - 2\times2\times\sqrt{5} + (\sqrt{5})^2$$

Step2: Calculate each term

Compute squares and product:
$$= 4 - 4\sqrt{5} + 5$$

Step3: Combine constant terms

Add the constant values:
$$= 4+5 - 4\sqrt{5} = 9 - 4\sqrt{5}$$

Answer:

$9 - 4\sqrt{5}$