Question

(-6+squareroot5)(-9-squareroot5)

Answer 1

To simplify the expression \((-6 + \sqrt{5})(-9 - \sqrt{5})\), we will use the distributive property (also known as the FOIL method for binomials).

Let's expand the expression step by step:

\[
(-6 + \sqrt{5})(-9 - \sqrt{5}) = (-6)(-9) + (-6)(-\sqrt{5}) + (\sqrt{5})(-9) + (\sqrt{5})(-\sqrt{5}).
\]

Now, we calculate each term:

1. \((-6)(-9) = 54\)
2. \((-6)(-\sqrt{5}) = 6\sqrt{5}\)
3. \((\sqrt{5})(-9) = -9\sqrt{5}\)
4. \((\sqrt{5})(-\sqrt{5}) = -5\)

Now we combine all the terms:

\[
54 + 6\sqrt{5} - 9\sqrt{5} - 5.
\]

Now, we can combine like terms:

- The constant terms: \(54 - 5 = 49\)
- The terms involving \(\sqrt{5}\): \(6\sqrt{5} - 9\sqrt{5} = -3\sqrt{5}\)

Putting it all together, we get:

\[
49 - 3\sqrt{5}.
\]

So, the simplified expression is:

\[
\boxed{49 - 3\sqrt{5}}.
\]