Question

(sqrt(5)-1)^2-(2sqrt(5)+1)^2

Answer 1

$(\sqrt{5}-1)^2-(2\sqrt{5}+1)^2=(\sqrt{5}-1+2\sqrt{5}+1)(\sqrt{5}-1-2\sqrt{5}-1)=\\ =3\sqrt{5}(-2-\sqrt{5})$

Answer 2

Let's simplify the expression step by step:

Given expression: (sqrt(5) - 1)^2 - (2sqrt(5) + 1)^2

Expanding the squares: = (5 - 2sqrt(5) + 1) - (4*5 + 4sqrt(5) + 1)

Simplifying the expression within parentheses: = (6 - 2sqrt(5)) - (20 + 4sqrt(5) + 1)

Combining like terms: = 6 - 2sqrt(5) - 20 - 4sqrt(5) - 1

= -15 - 6sqrt(5)

Therefore, the simplified form of the expression is -15 - 6sqrt(5).