Answer:
B
Step-by-step explanation:
Noting the following rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
Given
([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )
Each term in the second factor is multiplied by each term in the first factor
= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis
= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]
