ANSWER
[tex]2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}[/tex]
EXPLANATION
The given product is:
[tex]( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )[/tex]
We expand using the distributive property to obtain:
[tex]\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )[/tex]
Extract the perfect squares to get:
[tex]\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )[/tex]
Expand further to get;
[tex]2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21} [/tex]
This simplifies to,
[tex]2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21} [/tex]
