Pregunta
Multiply and simplify. \( (2 \sqrt{x}-\sqrt{3})(2 \sqrt{x}+\sqrt{3})=\square \) \( (\sqrt{x}-\sqrt{3})^{2}=\square \)
Ask by Love Mann. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( (2 \sqrt{x}-\sqrt{3})(2 \sqrt{x}+\sqrt{3}) = 4x - 3 \)
\( (\sqrt{x}-\sqrt{3})^{2} = x - 2\sqrt{3x} + 3 \)
Solución
Calculate or simplify the expression \( (2 \sqrt{x}-\sqrt{3})(2 \sqrt{x}+\sqrt{3}) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2\sqrt{x}-\sqrt{3}\right)\left(2\sqrt{x}+\sqrt{3}\right)\)
- step1: Simplify the product:
\(\left(2\sqrt{x}\right)^{2}-\left(\sqrt{3}\right)^{2}\)
- step2: Evaluate the power:
\(4x-3\)
Calculate or simplify the expression \( (\sqrt{x}-\sqrt{3})^{2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\sqrt{x}-\sqrt{3}\right)^{2}\)
- step1: Calculate:
\(x-2\sqrt{3x}+3\)
The simplified form of the expression \( (2 \sqrt{x}-\sqrt{3})(2 \sqrt{x}+\sqrt{3}) \) is \( 4x-3 \).
The simplified form of the expression \( (\sqrt{x}-\sqrt{3})^{2} \) is \( x-2\sqrt{3x}+3 \).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To multiply and simplify \( (2 \sqrt{x}-\sqrt{3})(2 \sqrt{x}+\sqrt{3}) \), we can use the difference of squares formula, \( a^2 - b^2 \): \[ (2 \sqrt{x})^2 - (\sqrt{3})^2 = 4x - 3 \] So, the first expression simplifies to \( 4x - 3 \). Now, for \( (\sqrt{x}-\sqrt{3})^{2} \), we can apply the square of a binomial formula \( (a-b)^2 = a^2 - 2ab + b^2 \): \[ (\sqrt{x})^2 - 2(\sqrt{x})(\sqrt{3}) + (\sqrt{3})^2 = x - 2\sqrt{3x} + 3 \] Thus, the second expression simplifies to \( x - 2\sqrt{3x} + 3 \).
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