Question

(2√3+1)(2+√3)-(√6+√2)^2 =

Answer 1

4v3+2*3+2+v3 - 6-2v12-2 = 5v3+8-6-2-2v4*3 = 5v3-4v3 = v3

Answer 2

To simplify the expression, let's take it step by step:

Step 1: Expand the expressions inside the parentheses. (2√3 + 1)(2 + √3) = 2√3 * 2 + 2√3 * √3 + 1 * 2 + 1 * √3 = 4√3 + 2√(3^2) + 2 + √3 = 4√3 + 6 + 2 + √3 = 5√3 + 8

(√6 + √2)^2 = (√6 + √2)(√6 + √2) = √6 * √6 + √6 * √2 + √2 * √6 + √2 * √2 = 6 + √12 + √12 + 2 = 6 + 2√3 + 2 = 8 + 2√3

Step 2: Now, substitute the simplified expressions back into the main expression: (2√3 + 1)(2 + √3) - (√6 + √2)^2 = (5√3 + 8) - (8 + 2√3)

Step 3: Combine like terms: (5√3 + 8) - (8 + 2√3) = 5√3 + 8 - 8 - 2√3

Step 4: Simplify further: 5√3 + 8 - 8 - 2√3 = 5√3 - 2√3

Step 5: Combine like terms again: 5√3 - 2√3 = 3√3

Therefore, the simplified expression is 3√3.