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\( x^{2} - 1 \) factors to \( (x - 1)(x + 1) \).
Solución
To factor the expression \( x^{2} - 1 \), you can recognize it as a **difference of squares**. A difference of squares has the general form:
\[
a^{2} - b^{2} = (a - b)(a + b)
\]
In your expression, \( x^{2} - 1 \), \( a = x \) and \( b = 1 \). Applying the difference of squares formula:
\[
x^{2} - 1 = (x - 1)(x + 1)
\]
**Factored Form:**
\[
(x - 1)(x + 1)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Mind Expander
Did you know that the expression \( x^{2}-1 \) is known as a difference of squares? This mathematical gem can be factored as \( (x-1)(x+1) \). It’s like breaking down a big task into two simpler ones, making it easier to solve equations or analyze functions. Now, let's put this baby to work! If you set \( x^{2}-1 = 0 \), you'll find the solutions are \( x = 1 \) and \( x = -1 \). This means anything more complicated can be simplified down to determining these roots, which has real-world applications in physics and engineering where finding limits or zeros can change the game!
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