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\( x^{2} - 36 = (x - 6)(x + 6) \)
Solución
To factorize the expression \( x^{2} - 36 \), you can recognize it as a **difference of squares**. The difference of squares follows the formula:
\[
a^{2} - b^{2} = (a - b)(a + b)
\]
Here, \( x^{2} \) is the square of \( x \), and \( 36 \) is the square of \( 6 \) (since \( 6^{2} = 36 \)). Applying the difference of squares formula:
\[
x^{2} - 36 = x^{2} - 6^{2} = (x - 6)(x + 6)
\]
**Final Factored Form:**
\[
x^{2} - 36 = (x - 6)(x + 6)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
You can factor the expression \( x^{2}-36 \) using the difference of squares formula, which states that \( a^{2}-b^{2} = (a-b)(a+b) \). Here, \( x^{2} \) is \( a^{2} \) and \( 36 \) is \( b^{2} \). So, you can rewrite it as \( (x-6)(x+6) \). When you factor, always remember to confirm by expanding: \( (x-6)(x+6) = x^{2} - 36 \). This is a quick way to verify that you've done it correctly!
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