Answer
$32+11\sqrt{2}$
Work Step by Step
RECALL:
Two binomials can be multiplied using the formula:
$(a+b)(c+d) = a(c+d) + b(c+d)=ac+ad+bc+bd$
The last expression, $ac+ad+bc+bd$, is what others refer to as the FOIL method of multiplying two binomials (the sum of the products of: First terms, Outer terms, Inner terms, and Last terms)
Use the formula above to obtain:
$=5(6)+5\sqrt{2}+6\sqrt{2}+\sqrt{2}\cdot\sqrt{2}
\\=30+(5\sqrt{2}+6\sqrt{2})+\sqrt{4}
\\=30+(5\sqrt{2}+6\sqrt{2})+2$
Simplify to obtain:
$=(30+2)+(5+6)\sqrt{2}
\\=32+11\sqrt{2}$
