To simplify the expression \(-2 \sqrt{48} + 4 \sqrt{3}\), we start by simplifying \(\sqrt{48}\).
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First, factor \(48\): \[ 48 = 16 \times 3 \] Thus, we can write: \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]
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Substitute \(\sqrt{48}\) in the expression: \[ -2 \sqrt{48} + 4 \sqrt{3} = -2(4\sqrt{3}) + 4\sqrt{3} \]
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Simplify further: \[ -2(4\sqrt{3}) = -8\sqrt{3} \] Therefore, the expression becomes: \[ -8\sqrt{3} + 4\sqrt{3} \]
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Combine like terms: \[ -8\sqrt{3} + 4\sqrt{3} = (-8 + 4)\sqrt{3} = -4\sqrt{3} \]
So, the final simplified result is: \[ \boxed{-4\sqrt{3}} \]