Question
Part 2 of 3 (b) \( (\sqrt{3}+\sqrt{q})(\sqrt{3}-\sqrt{q})=\square \)
Ask by Pollard Zimmerman. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (\sqrt{3}+\sqrt{q})(\sqrt{3}-\sqrt{q})=3-q \)
Solution
Calculate or simplify the expression \( (\sqrt{3}+\sqrt{q})(\sqrt{3}-\sqrt{q}) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\sqrt{3}+\sqrt{q}\right)\left(\sqrt{3}-\sqrt{q}\right)\)
- step1: Simplify the product:
\(\left(\sqrt{3}\right)^{2}-\left(\sqrt{q}\right)^{2}\)
- step2: Evaluate the power:
\(3-q\)
The expression \((\sqrt{3}+\sqrt{q})(\sqrt{3}-\sqrt{q})\) simplifies to \(3-q\).
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Simplify this solution The Deep Dive
This expression can be simplified using the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \). Here, let \( a = \sqrt{3} \) and \( b = \sqrt{q} \). Thus, we get: \[ (\sqrt{3}+\sqrt{q})(\sqrt{3}-\sqrt{q}) = (\sqrt{3})^2 - (\sqrt{q})^2 = 3 - q \] The final result is: \[ 3 - q \]
