Question

what are the factors of $x^2 - 100$?
○ $(x - 50)(x + 50)$
○ $(x - 10)(x + 10)$
○ $(x - 25)(x + 4)$
○ $(x - 5)(x + 20)$

Explanation:

Step1: Identify the formula

The expression \(x^2 - 100\) is a difference of squares, which follows the formula \(a^2 - b^2=(a - b)(a + b)\).

Step2: Apply the formula

Here, \(a = x\) and \(b^2 = 100\), so \(b=\sqrt{100}=10\). Substituting into the formula, we get \((x - 10)(x + 10)\). We can check by expanding: \((x - 10)(x + 10)=x^2+10x - 10x - 100=x^2 - 100\), which matches the original expression.

Answer:

B. \((x - 10)(x + 10)\)