# Divide (Q^4-1)/(Q+1)

Q4-1Q+1
Simplify the numerator.
Rewrite Q4 as (Q2)2.
(Q2)2-1Q+1
Rewrite 1 as 12.
(Q2)2-12Q+1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=Q2 and b=1.
(Q2+1)(Q2-1)Q+1
Simplify.
Rewrite 1 as 12.
(Q2+1)(Q2-12)Q+1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=Q and b=1.
(Q2+1)(Q+1)(Q-1)Q+1
(Q2+1)(Q+1)(Q-1)Q+1
(Q2+1)(Q+1)(Q-1)Q+1
Cancel the common factor of Q+1.
Cancel the common factor.
(Q2+1)(Q+1)(Q-1)Q+1
Divide (Q2+1)(Q-1) by 1.
(Q2+1)(Q-1)
(Q2+1)(Q-1)
Expand (Q2+1)(Q-1) using the FOIL Method.
Apply the distributive property.
Q2(Q-1)+1(Q-1)
Apply the distributive property.
Q2Q+Q2⋅-1+1(Q-1)
Apply the distributive property.
Q2Q+Q2⋅-1+1Q+1⋅-1
Q2Q+Q2⋅-1+1Q+1⋅-1
Simplify each term.
Multiply Q2 by Q by adding the exponents.
Multiply Q2 by Q.
Raise Q to the power of 1.
Q2Q1+Q2⋅-1+1Q+1⋅-1
Use the power rule aman=am+n to combine exponents.
Q2+1+Q2⋅-1+1Q+1⋅-1
Q2+1+Q2⋅-1+1Q+1⋅-1
Q3+Q2⋅-1+1Q+1⋅-1
Q3+Q2⋅-1+1Q+1⋅-1
Move -1 to the left of Q2.
Q3-1⋅Q2+1Q+1⋅-1
Rewrite -1Q2 as -Q2.
Q3-Q2+1Q+1⋅-1
Multiply Q by 1.
Q3-Q2+Q+1⋅-1
Multiply -1 by 1.
Q3-Q2+Q-1
Q3-Q2+Q-1
Divide (Q^4-1)/(Q+1)