Question

question
express the product $(10 - \sqrt{3})(10 - \sqrt{3})$ in simplest form.

Explanation:

Step1: Recognize perfect square

$(10 - \sqrt{3})(10 - \sqrt{3}) = (10 - \sqrt{3})^2$

Step2: Apply square of difference formula

Recall $(a-b)^2 = a^2 - 2ab + b^2$, so:
$(10 - \sqrt{3})^2 = 10^2 - 2(10)(\sqrt{3}) + (\sqrt{3})^2$

Step3: Calculate each term

$10^2 = 100$, $2(10)(\sqrt{3}) = 20\sqrt{3}$, $(\sqrt{3})^2 = 3$

Step4: Combine terms

$100 - 20\sqrt{3} + 3 = 103 - 20\sqrt{3}$

Answer:

$103 - 20\sqrt{3}$