Multiply and simplify the following radical expressions.

(5√2 − √5)(5√2 − 5√5)

(5√2 − √5)(5√2 − 5√5)

= 50 - 25√10 - 5√10 + 25

collect your like terms and simplify

To multiply and simplify the given radical expressions (5√2 - √5)(5√2 - 5√5), you can use the FOIL method.

FOIL stands for First, Outer, Inner, and Last. It is a method used to multiply two binomials.

First, multiply the first terms of each binomial:
(5√2) * (5√2) = 25 * (√2 * √2) = 25 * 2 = 50.

Outer, multiply the outer terms of each binomial:
(5√2) * (-5√5) = -25 * (√10).

Inner, multiply the inner terms of each binomial:
(-√5) * (5√2) = -25 * (√10).

Last, multiply the last terms of each binomial:
(-√5) * (-5√5) = 25 * 5 = 125.

Combine the results:
50 - 25√10 - 25√10 + 125.

Simplify the like terms:
50 - 50√10 + 125.

Combine the constants:
175 - 50√10.

So, the simplified expression is 175 - 50√10.

To multiply and simplify the given radical expressions, we will use the distributive property.

Step 1: Distribute the first term (5√2) to both terms in the second expression (5√2 − 5√5):

(5√2)(5√2) − (5√2)(5√5)

Step 2: Distribute the second term (−√5) to both terms in the second expression (5√2 − 5√5):

(−√5)(5√2) − (−√5)(5√5)

Step 3: Simplify each multiplication:

(25√4) − (25√10) − (5√10) + (5√25)

Step 4: Simplify the square roots:

(25√4) simplifies to (25 * 2) = 50

√10 cannot be simplified further

−(25√10) simplifies to −(25 * √10)

−√10 cannot be simplified further

(5√25) simplifies to (5 * 5) = 25

Step 5: Combine like terms:

50 − 25√10 − 5√10 + 25

Step 6: Simplify further:

Combine the numbers: 50 + 25 = 75

Combine the square roots: −25√10 − 5√10 = −30√10

Final Answer: 75 − 30√10