(5+h)3-125h

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

Add h and 0.

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

Add 5h and 5h.

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

Add 25 and 25.

h(10h+h2+50+5h+25)h

Add 10h and 5h.

h(15h+h2+50+25)h

Add 50 and 25.

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.

h(h2+15h+75)h

Divide h2+15h+75 by 1.

h2+15h+75

h2+15h+75

Simplify ((5+h)^3-125)/h