Question
Simplify the following Expression. \[ (\sqrt{x}+9)(\sqrt{x}-3)=\square \]
Ask by Young Carroll. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( x + 6\sqrt{x} - 27 \).
Solution
Calculate or simplify the expression \( (\sqrt{x}+9)(\sqrt{x}-3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\sqrt{x}+9\right)\left(\sqrt{x}-3\right)\)
- step1: Use the distributive property:
\(\sqrt{x}\times \sqrt{x}+\sqrt{x}\times \left(-3\right)+9\sqrt{x}+9\left(-3\right)\)
- step2: Calculate the product:
\(x+\sqrt{x}\times \left(-3\right)+9\sqrt{x}+9\left(-3\right)\)
- step3: Calculate:
\(x-3\sqrt{x}+9\sqrt{x}+9\left(-3\right)\)
- step4: Multiply the numbers:
\(x-3\sqrt{x}+9\sqrt{x}-27\)
- step5: Calculate:
\(x+6\sqrt{x}-27\)
The simplified expression is \(x+6\sqrt{x}-27\).
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Simplify this solution Extra Insights
To simplify the expression, we can use the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \). Here, \( a = \sqrt{x} \) and \( b = 3 \). Using the formula, we get: \[ (\sqrt{x}+9)(\sqrt{x}-3) = \sqrt{x}^2 - 3^2 + 9\sqrt{x} - 27 \] Calculating \( \sqrt{x}^2 \) gives us \( x \) and \( 3^2 \) gives us \( 9 \): \[ = x - 9 + 9\sqrt{x} - 27 \] Combining like terms results in: \[ = x + 9\sqrt{x} - 36 \] So, the simplified expression is: \[ = x + 9\sqrt{x} - 36 \] Now you can confidently present the simplified expression to anyone!
