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A expressão simplificada é \(8\sqrt{5} - 12\sqrt{10}\).
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To simplify \( 4(\sqrt{20}-\sqrt{90}) \), we start by simplifying the square roots: \[ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \] \[ \sqrt{90} = \sqrt{9 \cdot 10} = 3\sqrt{10} \] Now substituting these back into the expression, we get: \[ 4(2\sqrt{5} - 3\sqrt{10}) \] Distributing the 4 gives us: \[ 8\sqrt{5} - 12\sqrt{10} \] So, the simplified expression is: \[ 8\sqrt{5} - 12\sqrt{10} \]
