Question

Multiply. Write your answer in simplest form.
(-10 squareroot21 + squareroot3) (-8 squareroot2 - squareroot21)

Answer 1

To multiply the expression \((-10 \sqrt{21} + \sqrt{3})(-8 \sqrt{2} - \sqrt{21})\), we can use the distributive property (also known as the FOIL method for binomials). Let's multiply each term:

1. **Multiply the first terms:**
\[
(-10 \sqrt{21})(-8 \sqrt{2}) = 80 \sqrt{42}
\]

2. **Multiply the outer terms:**
\[
(-10 \sqrt{21})(-\sqrt{21}) = 10 \cdot 21 = 210
\]

3. **Multiply the inner terms:**
\[
(\sqrt{3})(-8 \sqrt{2}) = -8 \sqrt{6}
\]

4. **Multiply the last terms:**
\[
(\sqrt{3})(-\sqrt{21}) = -\sqrt{63} = -3\sqrt{7}
\]

Now, we combine all these results:
\[
80\sqrt{42} + 210 - 8\sqrt{6} - 3\sqrt{7}
\]

Putting it all together, we have:
\[
210 + 80\sqrt{42} - 8\sqrt{6} - 3\sqrt{7}
\]

This expression is in its simplest form. Thus, our final answer is:
\[
\boxed{210 + 80\sqrt{42} - 8\sqrt{6} - 3\sqrt{7}}
\]