# Simplify ((5+h)^3-125)/h (5+h)3-125h
Simplify the numerator.
Rewrite 125 as 53.
(5+h)3-53h
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=5+h and b=5.
(5+h-5)((5+h)2+(5+h)⋅5+52)h
Simplify.
Subtract 5 from 5.
(h+0)((5+h)2+(5+h)⋅5+52)h
h((5+h)2+(5+h)⋅5+52)h
Rewrite (5+h)2 as (5+h)(5+h).
h((5+h)(5+h)+(5+h)⋅5+52)h
Expand (5+h)(5+h) using the FOIL Method.
Apply the distributive property.
h(5(5+h)+h(5+h)+(5+h)⋅5+52)h
Apply the distributive property.
h(5⋅5+5h+h(5+h)+(5+h)⋅5+52)h
Apply the distributive property.
h(5⋅5+5h+h⋅5+h⋅h+(5+h)⋅5+52)h
h(5⋅5+5h+h⋅5+h⋅h+(5+h)⋅5+52)h
Simplify and combine like terms.
Simplify each term.
Multiply 5 by 5.
h(25+5h+h⋅5+h⋅h+(5+h)⋅5+52)h
Move 5 to the left of h.
h(25+5h+5⋅h+h⋅h+(5+h)⋅5+52)h
Multiply h by h.
h(25+5h+5h+h2+(5+h)⋅5+52)h
h(25+5h+5h+h2+(5+h)⋅5+52)h
h(25+10h+h2+(5+h)⋅5+52)h
h(25+10h+h2+(5+h)⋅5+52)h
Apply the distributive property.
h(25+10h+h2+5⋅5+h⋅5+52)h
Multiply 5 by 5.
h(25+10h+h2+25+h⋅5+52)h
Move 5 to the left of h.
h(25+10h+h2+25+5⋅h+52)h
Raise 5 to the power of 2.
h(25+10h+h2+25+5h+25)h
h(10h+h2+50+5h+25)h
h(15h+h2+50+25)h
h(15h+h2+75)h
Reorder terms.
h(h2+15h+75)h
h(h2+15h+75)h
h(h2+15h+75)h
Cancel the common factor of h.
Cancel the common factor.
h(h2+15h+75)h
Divide h2+15h+75 by 1.
h2+15h+75
h2+15h+75
Simplify ((5+h)^3-125)/h     