What is expand A/(S+1)*(S+1)(S-1)(S+2)(S^2+1) ?

The solution to expand A/(S+1)*(S+1)(S-1)(S+2)(S^2+1) is AS^4-AS^2+AS+AS^3-2A

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expand A/(S+1)*(S+1)(S-1)(S+2)(S^2+1)

expand

\frac{A}{S + 1} \cdot (S + 1) (S - 1) (S + 2) (S^{2} + 1)

A S^{4} - A S^{2} + A S + A S^{3} - 2 A

Solution steps

\frac{A}{S + 1} (S + 1) (S - 1) (S + 2) (S^{2} + 1)

Expand

\frac{A}{S + 1} (S + 1) (S - 1) (S + 2) (S^{2} + 1) : \frac{A}{S + 1} (S^{2} - 1) (S + 2) (S^{2} + 1)

= \frac{A}{S + 1} (S^{2} - 1) (S + 2) (S^{2} + 1)

Apply Difference of Two Squares

(S^{2} - 1) (S^{2} + 1) : S^{4} - 1

= \frac{A}{S + 1} (S^{4} - 1) (S + 2)

Apply FOIL method

(S^{4} - 1) (S + 2) : S^{5} + 2 S^{4} - S - 2

= \frac{A}{S + 1} (S^{5} + 2 S^{4} - S - 2)

Distribute parentheses

= \frac{A}{S + 1} S^{5} + \frac{A}{S + 1} \cdot 2 S^{4} + \frac{A}{S + 1} (- S) + \frac{A}{S + 1} (- 2)

Simplify

\frac{A}{S + 1} S^{5} + \frac{A}{S + 1} \cdot 2 S^{4} + \frac{A}{S + 1} (- S) + \frac{A}{S + 1} (- 2) : A S^{4} - A S^{2} + A S + A S^{3} - 2 A

= A S^{4} - A S^{2} + A S + A S^{3} - 2 A

(\frac{x}{n} - \frac{1}{n})^{3}

(10 - y) (\frac{y}{3} + 8)

7 x^{\frac{7}{5}} (x^{\frac{11}{5}} - 2 x)

What is expand A/(S+1)*(S+1)(S-1)(S+2)(S^2+1) ?
The solution to expand A/(S+1)*(S+1)(S-1)(S+2)(S^2+1) is AS^4-AS^2+AS+AS^3-2A