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\( u^{2} - 9 = (u - 3)(u + 3) \)
Solución
To factor the quadratic expression \( u^{2} - 9 \), you can recognize it as a **difference of squares**. The difference of squares follows the pattern:
\[
a^{2} - b^{2} = (a - b)(a + b)
\]
In your case:
- \( a = u \)
- \( b = 3 \) (since \( 3^{2} = 9 \))
Applying the pattern:
\[
u^{2} - 9 = (u - 3)(u + 3)
\]
**Factored Form:**
\[
(u - 3)(u + 3)
\]
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Simplifique esta solución Beyond the Answer
To factor \( u^{2}-9 \), you can recognize this as a difference of squares, which follows the formula \( a^{2} - b^{2} = (a + b)(a - b) \). In this case, \( u^{2} \) is \( a^{2} \) and \( 9 \) is \( 3^{2} \). Therefore, you can rewrite it as: \[ u^{2} - 3^{2} = (u + 3)(u - 3) \] And there you have it! The factored form is \( (u + 3)(u - 3) \). Happy factoring!
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