ANSWER
EXPLANATION
We want to simplify:
[tex](2\sqrt{5}+3)(\sqrt{5}-1)[/tex]
Recall the distributive property;
(a+b)(c+d)=a(c+d)+b(c+d)
We apply this property to get,
[tex]2\sqrt{5}(\sqrt{5}-1) + 3(\sqrt{5}-1)[/tex]
We expand to get,
[tex]2 \times 5-2 \sqrt{5} + 3\sqrt{5}-3[/tex]
This simplifies to,
[tex]10 + \sqrt{5}-3[/tex]
The simplest form of the given expression is:
[tex]7 + \sqrt{5}[/tex]
