Answer:
Option d
[tex](2\sqrt{5}-4)(3\sqrt{5}+2)=22 -8\sqrt{5}[/tex]
Step-by-step explanation:
We have an expression composed of the product of 2 factors:
[tex](2\sqrt{5}-4)(3\sqrt{5}+2)[/tex]
To simplify the expression we use the distributive property
[tex](2\sqrt{5}-4)(3\sqrt{5}+2) = 2\sqrt{5}(3\sqrt{5}) +2\sqrt{5}(2) -4(3\sqrt{5}) -4(2)[/tex]
Simplifying we obtain:
[tex](2\sqrt{5}-4)(3\sqrt{5}+2)=6(5) +4\sqrt{5} -12\sqrt{5} -8\\\\(2\sqrt{5}-4)(3\sqrt{5}+2)=30 -8\sqrt{5} -8\\\\(2\sqrt{5}-4)(3\sqrt{5}+2)=22 -8\sqrt{5}[/tex]
The answer is the option d.
