(3√5 − 5√2)(4√5 + 3√2)

Sure, let's solve this step by step:

First, we need to apply the distributive property (a(b + c) = ab + ac) to the expression:

(3√5 − 5√2)(4√5 + 3√2) = 3√5 * 4√5 + 3√5 * 3√2 - 5√2 * 4√5 - 5√2 * 3√2

Next, we simplify each term:

= 12 * 5 + 9 * √10 - 20 * √10 - 15 * 2

= 60 + 9√10 - 20√10 - 30

= 30 - 11√10

So, (3√5 − 5√2)(4√5 + 3√2) = 30 - 11√10.