Introductory Algebra for College Students (7th Edition)

$25-2\sqrt{5}$
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: $=40+(-12+10)\sqrt{5}-3(5) \\=40+(-2\sqrt{5})-15 \\=(40-15)-2\sqrt{5} \\=25-2\sqrt{5}$