please simplify the radical expression (-3 - 5 sqrt 2)(3+sqrt 2)

Question

Thank you

Answer 1

Multiply the two 'binomials' using FOIL:

f:  -9

o: -3√2
i: -15√2

l: -10

 

Combine the integers and combine the two surds; you get -19-19√2.

 

Check your work!  (You can check it decimally...a very good technique, using calculator)