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
Factor the expression \( 9x^2-100 \).
Factor the expression by following steps:
- step0: Factor:
\(9x^{2}-100\)
- step1: Rewrite the expression:
\(\left(3x\right)^{2}-10^{2}\)
- step2: Factor the expression:
\(\left(3x-10\right)\left(3x+10\right)\)
The difference of two squares \(9x^{2}-100\) can be factored as \((3x-10)(3x+10)\).
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Simplify this solution 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 \( (3x - 10)(3x + 10) \).
