Question

Multiply. Write your answer in simplest form.
(-10 + 10 squareroot11) (-8 + 8 squareroot7)

Answer 1

To multiply the two expressions \((-10 + 10\sqrt{11})\) and \((-8 + 8\sqrt{7})\), we can use the distributive property (also known as the FOIL method for binomials):

\[
(-10 + 10\sqrt{11})(-8 + 8\sqrt{7}) = (-10)(-8) + (-10)(8\sqrt{7}) + (10\sqrt{11})(-8) + (10\sqrt{11})(8\sqrt{7})
\]

Now we will compute each term:

1. \((-10)(-8) = 80\)
2. \((-10)(8\sqrt{7}) = -80\sqrt{7}\)
3. \((10\sqrt{11})(-8) = -80\sqrt{11}\)
4. \((10\sqrt{11})(8\sqrt{7}) = 80\sqrt{77}\)

Putting it all together, we have:

\[
80 - 80\sqrt{7} - 80\sqrt{11} + 80\sqrt{77}
\]

Now, we can combine the terms:

The expression is:

\[
80 + 80\sqrt{77} - 80\sqrt{7} - 80\sqrt{11}
\]

We can factor out the common factor of \(80\):

\[
80 + 80(\sqrt{77} - \sqrt{7} - \sqrt{11})
\]

Thus, the final answer in simplest form is:

\[
\boxed{80(1 + \sqrt{77} - \sqrt{7} - \sqrt{11})}
\]