To simplify the expression \(-4\sqrt{160} - 2\sqrt{90}\), we first break down each radical.
Step 1: Simplify \(\sqrt{160}\)
\[ 160 = 16 \times 10 = 4^2 \times 10 \] So, \[ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10} \] Thus, \[ -4\sqrt{160} = -4(4\sqrt{10}) = -16\sqrt{10} \]
Step 2: Simplify \(\sqrt{90}\)
\[ 90 = 9 \times 10 = 3^2 \times 10 \] So, \[ \sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10} \] Thus, \[ -2\sqrt{90} = -2(3\sqrt{10}) = -6\sqrt{10} \]
Step 3: Combine the simplified terms
Now we combine \(-16\sqrt{10}\) and \(-6\sqrt{10}\): \[ -16\sqrt{10} - 6\sqrt{10} = (-16 - 6)\sqrt{10} = -22\sqrt{10} \]
Final Answer:
The simplified result is \[ \boxed{-22\sqrt{10}} \]