Question

Вычислите (4√2-2√3)(6√2+3√3)-(1-√3)(√3+1)

Answer 1

(4√2-2√3)(6√2+3√3)-(1-√3)(√3+1) = (4*6*2+3*4*√6-2*6√6-6*3)-(√3+1-3-√3)=48+12√6-12√6-18-√3+2+√3=32

Answer 2

First, let's simplify the expression step by step:

1. Distribute the terms inside the first parentheses: (4√2 - 2√3)(6√2 + 3√3) = 24√4 + 12√6 - 12√6 - 6√9

2. Simplify the square roots: √4 = 2 √6 cannot be simplified further √9 = 3

Therefore, the expression becomes: 24(2) + 12√6 - 12√6 - 6(3)

3. Combine like terms: 48 + 12√6 - 12√6 - 18

4. Simplify further: 48 - 18 = 30 12√6 - 12√6 = 0

The expression simplifies to: 30

Now, let's simplify the second part of the expression:

1. Distribute the terms inside the second parentheses: (1 - √3)(√3 + 1) = √3 + 1 - √3 - 1

2. Simplify further: √3 - √3 = 0 1 - 1 = 0

The expression simplifies to: 0

Finally, let's subtract the two simplified expressions:

30 - 0 = 30

Therefore, the result of the expression (4√2 - 2√3)(6√2 + 3√3) - (1 - √3)(√3 + 1) is 30.