Question
Factor the difference of two squares: \( 9 x^{2}-100 \)
Ask by Wade Mejia. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(9x^2 - 100 = (3x - 10)(3x + 10)\)
Solution
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Bonus Knowledge
To factor the expression \( 9x^{2} - 100 \), we can recognize that it is a difference of two squares. We can rewrite it as: \[ (3x)^{2} - 10^{2} \] Now, we apply the difference of squares formula, which states that \( a^{2} - b^{2} = (a - b)(a + b) \). Here, \( a = 3x \) and \( b = 10 \). Therefore, we can factor it as: \[ (3x - 10)(3x + 10) \] And there you have it! The expression \( 9x^{2} - 100 \) factors to \( (3x - 10)(3x + 10) \).
