Answer:
[tex](3\sqrt{3} -2\sqrt{2})^2=35-12\sqrt{6}[/tex]
Step-by-step explanation:
Using the FOIL method:
[tex]F+O+I+L[/tex]
Simplify the expression by squaring:
[tex](3\sqrt{3}-2\sqrt{2} )(3\sqrt{3}-2\sqrt{2})[/tex]
Now we can use the Foil method:
First, Outside, Inside, Last
Multiply the first terms within each grouping:
[tex]3\sqrt{3}*3\sqrt{3} \\\\3*3\sqrt{3*3} \\\\9\sqrt{9} \\\\9*3\\\\27[/tex]
Insert as the first term:
[tex]27+O+I+L[/tex]
Now multiply the outside terms in each grouping:
[tex]3\sqrt{3} *(-2\sqrt{2})\\\\-3*2\sqrt{3*2} \\\\-6\sqrt{6}[/tex]
Insert as the next term:
[tex]27-6\sqrt{6} +I+L[/tex]
Now multiply the inside terms:
[tex]-2\sqrt{2} *3\sqrt{3} \\\\-2*3\sqrt{2*3} \\\\-6\sqrt{6}[/tex]
Insert as the third term:
[tex]27-6\sqrt{6} -6\sqrt{6}+L[/tex]
Now multiply the last terms in the grouping:
[tex]-2\sqrt{2} *(-2\sqrt{2} )\\\\-2*(-2)\sqrt{2*2}\\\\ 4\sqrt{4}\\\\4*2\\\\8[/tex]
Insert as the last term:
[tex]27-6\sqrt{6} -6\sqrt{6}+8[/tex]
Simplify by combining like terms:
[tex]27+8-6\sqrt{6} -6\sqrt{6}\\\\35-12\sqrt{6}[/tex]
:Done
