Answer:
12[tex]\sqrt{6}[/tex] + 8[tex]\sqrt{15}[/tex] + 12 + 4[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
(4[tex]\sqrt{3}[/tex] + 2[tex]\sqrt{2}[/tex] )(3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{5}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
4[tex]\sqrt{3}[/tex] (3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{5}[/tex] ) + 2[tex]\sqrt{2}[/tex] (3[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{5}[/tex] ) ← distribute both parenthesis
= 12[tex]\sqrt{6}[/tex] + 8[tex]\sqrt{15}[/tex] + 12 + 4[tex]\sqrt{10}[/tex]
