Question

HELP ME!!! (4+√2)^2 - 4√8 = ?1 - (2√7+8) × (2√7 -8) = ?

Answer 1

(4+√2)^2 - 4√8 = 16 + 2*4*√2 + 2 - 4√8 = 16 + 8√2 + 2 - 4√8 =
18 + 8√2 - 4√8 = 18 + 8√2 - 4√4*2 = 18 + 8√2 - 8√2 = 18.

1 - (2√7+8)*(2√7 -8) = 1 - (2√7)² - 64 = - 63 - (√4*7)² = - 63 - (√28)² =
- 63 - 28 = - 91.

Answer 2

Let's break down each expression step by step:

Expression 1: (4+√2)^2 - 4√8

Step 1: Square the term inside the parentheses. (4+√2)^2 = (4+√2)(4+√2) = 16 + 8√2 + 8√2 + 2 = 16 + 16√2 + 2 = 18 + 16√2

Step 2: Simplify the second term. 4√8 = 4√(4 * 2) = 4√4√2 = 4 * 2√2 = 8√2

Now we can substitute these values back into the original expression: (4+√2)^2 - 4√8 = (18 + 16√2) - 8√2 = 18 + 16√2 - 8√2 = 18 + 8√2

Therefore, (4+√2)^2 - 4√8 simplifies to 18 + 8√2.

Expression 2: 1 - (2√7+8) × (2√7 - 8)

Step 1: Multiply the terms inside the parentheses. (2√7+8) × (2√7 - 8) = (2√7)(2√7) + (2√7)(-8) + (8)(2√7) + (8)(-8) = 4√7 * 2√7 - 16√7 + 16√7 - 64 = 8√49 - 64 = 8 * 7 - 64 = 56 - 64 = -8

Step 2: Substitute the result back into the original expression: 1 - (2√7+8) × (2√7 - 8) = 1 - (-8) = 1 + 8 = 9

Therefore, 1 - (2√7+8) × (2√7 - 8) simplifies to 9.