Question
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Tutor-Verified Answer
Answer
\(4(w-2)(w+2)\)
Solution
Factor the expression \( 4w^{2}-16 \).
Factor the expression by following steps:
- step0: Factor:
\(4w^{2}-16\)
- step1: Factor the expression:
\(4\left(w^{2}-4\right)\)
- step2: Factor the expression:
\(4\left(w-2\right)\left(w+2\right)\)
The factored form of \(4w^{2}-16\) is \(4(w-2)(w+2)\).
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Simplify this solution Beyond the Answer
To factor \( 4w^2 - 16 \) completely, first notice that both terms share a common factor of 4. So, we can factor out the 4: \( 4(w^2 - 4) \). Now, the expression inside the parentheses, \( w^2 - 4 \), is a difference of squares, which can be factored further: \( w^2 - 4 = (w - 2)(w + 2) \). Putting it all together, we get: \( 4(w - 2)(w + 2) \) as the completely factored form.
