(sqrt2-4)(5sqrt10+4)?

-16 + 4√2 + 10√5 - 20√10

Just bear these in mind, you'll be ok
√a√a = a
√a√b <=> √(ab)
(c√d)(e√f) <=> ce√(df)
(c√d) + (e√d) = (c+e)√d

( √2 - 4 ) (5√10 + 4 )

5√20 + 4√2 - 20√10 - 16

10√5 + 4√2 - 20√10 - 16

(√2 - 4)(5√10 + 4)
= 5√(2 * 10) - 4*5√10 + 4*√2 - 4*4
= 5√20 - 20√10 + 4√2 - 16
= 5√(2^2 * 5) - 20√10 + 4√2 - 16
= 5(2)√5 - 20√10 + 4√2 - 16
= 10√5 - 20√10 + 4√2 - 16
= 2(5√5 - 10√10 + 2√2 - 8)

10sqrt5 + 4sqrt2 -20sqrt10 -16

(sqrt(2)-4)(5sqrt(10)+4)

using FOIL:

= 5sqrt(20) + 4sqrt(2) - 20sqrt(10) - 16
= 5sqrt(4*5) + 4sqrt(2) - 20sqrt(10) - 16
= 10sqrt(5) + 4sqrt(2) - 20sqrt(10) - 16

10sqrt5+4sqrt2-20sqrt10-16