Which of the following expresses $16 \sqrt{10}+2 \sqrt{10}+\sqrt{40}-\sqrt{90}$ in simplest form? a) $-20 \sqrt{10}$ b) $20 \sqrt{10}$ c) $17 \sqrt{10}$ d) $-17 \sqrt{10}$

Step 1 ：The question is asking to simplify the expression \(16 \sqrt{10}+2 \sqrt{10}+\sqrt{40}-\sqrt{90}\).

Step 2 ：First, we can combine like terms \(16 \sqrt{10}+2 \sqrt{10}\) to get \(18 \sqrt{10}\).

Step 3 ：Next, we can simplify \(\sqrt{40}\) and \(\sqrt{90}\) by factoring out the largest perfect square from each.

Step 4 ：\(\sqrt{40}\) can be written as \(\sqrt{4*10}\), which simplifies to \(2\sqrt{10}\).

Step 5 ：\(\sqrt{90}\) can be written as \(\sqrt{9*10}\), which simplifies to \(3\sqrt{10}\).

Step 6 ：So, the expression becomes \(18 \sqrt{10} + 2\sqrt{10} - 3\sqrt{10}\).

Step 7 ：Finally, we can combine these terms to get the simplest form.

Step 8 ：The simplest form of the expression \(16 \sqrt{10}+2 \sqrt{10}+\sqrt{40}-\sqrt{90}\) is \(\boxed{17 \sqrt{10}}\). So, the correct option is c) \(17 \sqrt{10}\).