Question

difference of perfect squares (level 1)
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factor completely.
$100 - x^2$

Explanation:

Step1: Recall the difference of squares formula

The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Identify \(a\) and \(b\) in \(100 - x^2\)

We can rewrite \(100\) as \(10^2\), so in the expression \(100 - x^2\), we have \(a = 10\) and \(b=x\) since \(100 - x^2=10^2 - x^2\).

Step3: Apply the difference of squares formula

Substitute \(a = 10\) and \(b = x\) into the formula \(a^2 - b^2=(a + b)(a - b)\). We get \(10^2 - x^2=(10 + x)(10 - x)\).

Answer:

\((10 + x)(10 - x)\)