Factoring Polynomial Expression

Factor.

100(h + 1)^3 - (h + 1)^5

100(h+1)^(3)-(h+1)^(5)

Factor out the GCF of (h+1)^(3) from each term in the polynomial.
(h+1)^(3)(100)+(h+1)^(3)(-(h+1)^(2))

Factor out the GCF of (h+1)^(3) from 100(h+1)^(3)-(h+1)^(5).
(h+1)^(3)(100-(h+1)^(2))

The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(h+1)^(3)(10-(h+1))(10+(h+1))

Multiply -1 by each term inside the parentheses.
(h+1)^(3)(10+(-h-1))(10+(h+1))

Subtract 1 from 10 to get 9.
(h+1)^(3)(9-h)(10+(h+1))

Reorder the polynomial 9-h alphabetically from left to right, starting with the highest order term.
(h+1)^(3)(-h+9)(10+(h+1))

Remove the parentheses around the expression h+1.
(h+1)^(3)(-h+9)(10+h+1)

Add 1 to 10 to get 11.
(h+1)^(3)(-h+9)(11+h)

Reorder the polynomial 11+h alphabetically from left to right, starting with the highest order term.
(h+1)^(3)(-h+9)(h+11)

100(h+1)^3 - (h+1)^5

Substitute n for (h+1) for the time being.

100n^3 - n^5
= n^3(100-n^2)
= n^3(10+n)(10-n)

Replace n with (h+1) again.

(h+1)^3 (10+(h+1)) (10-(h+1))
= (h+1)^3 (10+h+1) (10-h-1)
= (h+1)^3 (11+h) (9-h)

Answer: (h+1)^3 (11+h)(9-h)

(h + 1)^3 (100 - (h + 1)^2) = (h + 1)^3 (10 - (h + 1))(10 + (h + 1)) = (h + 1)^3 (9 - h)(11 + h)