Question

Multiply. Write your answer in simplest form.
(squareroot39 - 7 squareroot15) (8 - squareroot2)

Answer 1

To multiply the expression \((\sqrt{39} - 7\sqrt{15})(8 - \sqrt{2})\), we will use the distributive property (also known as the FOIL method for binomials).

1. Multiply \(\sqrt{39}\) by \(8\):
\[
\sqrt{39} \cdot 8 = 8\sqrt{39}
\]

2. Multiply \(\sqrt{39}\) by \(-\sqrt{2}\):
\[
\sqrt{39} \cdot (-\sqrt{2}) = -\sqrt{78}
\]

3. Multiply \(-7\sqrt{15}\) by \(8\):
\[
-7\sqrt{15} \cdot 8 = -56\sqrt{15}
\]

4. Multiply \(-7\sqrt{15}\) by \(-\sqrt{2}\):
\[
-7\sqrt{15} \cdot (-\sqrt{2}) = 7\sqrt{30}
\]

Now, combine all these results together:
\[
8\sqrt{39} - \sqrt{78} - 56\sqrt{15} + 7\sqrt{30}
\]

Finally, the expression in combined form is:
\[
8\sqrt{39} - \sqrt{78} - 56\sqrt{15} + 7\sqrt{30}
\]

Since there are no like terms, this is already in its simplest form. Thus, the final answer is:
\[
8\sqrt{39} - \sqrt{78} - 56\sqrt{15} + 7\sqrt{30}
\]