Question

show all the steps it took to get your answer.
Multiply and simplify if possible
(5-sqrt 2)(4+sqrt 2)

Answer 1

To solve this problem, we will use the distributive property to multiply each term in the first expression by each term in the second expression.

Step 1: Multiply 5 by 4
5 * 4 = 20

Step 2: Multiply 5 by sqrt 2
5 * sqrt 2 = 5sqrt 2

Step 3: Multiply -sqrt 2 by 4
-sqrt 2 * 4 = -4sqrt 2

Step 4: Multiply -sqrt 2 by sqrt 2
-sqrt 2 * sqrt 2 = -2

Now, combine all the terms:

20 + 5sqrt 2 - 4sqrt 2 - 2

Step 5: Combine like terms
20 + (5 - 4)sqrt 2 - 2
= 20 + sqrt 2 - 2
= 18 + sqrt 2

Therefore, (5 - sqrt 2)(4 + sqrt 2) simplifies to 18 + sqrt 2.