Question

which expression is equivalent to ((5 - sqrt{3})^2)?
a (28)
b (28 - 5sqrt{3})
c (28 - 10sqrt{3})
d (22)

Explanation:

Step1: Apply square of difference formula

Recall $(a-b)^2=a^2-2ab+b^2$. Here $a=5$, $b=\sqrt{3}$.
$$(5-\sqrt{3})^2=5^2 - 2\times5\times\sqrt{3} + (\sqrt{3})^2$$

Step2: Calculate each term

Compute squares and product:
$$5^2=25,\ 2\times5\times\sqrt{3}=10\sqrt{3},\ (\sqrt{3})^2=3$$

Step3: Combine the terms

Sum the calculated values:
$$25 - 10\sqrt{3} + 3 = 28 - 10\sqrt{3}$$

Answer:

C. $28-10\sqrt{3}$