Answer
$25-2\sqrt{5}$
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:
$=4(10)-4(3\sqrt{5})+10\sqrt{5}-\sqrt{5}(3\sqrt{5})
\\=40-12\sqrt{5}+10\sqrt{5}-3\sqrt{25}
\\=40+(-12\sqrt{5}+10\sqrt{5})-3\sqrt{5^2}$
Simplify to obtain:
$=40+(-12+10)\sqrt{5}-3(5)
\\=40+(-2\sqrt{5})-15
\\=(40-15)-2\sqrt{5}
\\=25-2\sqrt{5}$
