Q4-1Q+1

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.

(Q2+1)(Q+1)(Q-1)Q+1

Divide (Q2+1)(Q-1) by 1.

(Q2+1)(Q-1)

(Q2+1)(Q-1)

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

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

Add 2 and 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)