Question

Find the continued product
(x+1)(x-1)(x^2+1)

Answer 1

Answer:

How to solve your problem

(+1)(−1)(2+1)

(x+1)(x-1)(x^{2}+1)(x+1)(x−1)(x2+1)

Simplify

1

Distribute

(+1)(−1)(2+1)

{\color{#c92786}{(x+1)(x-1)(x^{2}+1)}}(x+1)(x−1)(x2+1)

(2+1)(−1)+1(2+1)(−1)

{\color{#c92786}{x(x^{2}+1)(x-1)+1(x^{2}+1)(x-1)}}x(x2+1)(x−1)+1(x2+1)(x−1)

2

Distribute

(2+1)(−1)+1(2+1)(−1)

{\color{#c92786}{x(x^{2}+1)(x-1)}}+1(x^{2}+1)(x-1)x(x2+1)(x−1)+1(x2+1)(x−1)

(−1)⋅3+(−1)+1(2+1)(−1)

{\color{#c92786}{(x-1) \cdot x^{3}+x(x-1)}}+1(x^{2}+1)(x-1)(x−1)⋅x3+x(x−1)+1(x2+1)(x−1)

3

Distribute

(−1)⋅3+(−1)+1(2+1)(−1)

{\color{#c92786}{(x-1) \cdot x^{3}}}+x(x-1)+1(x^{2}+1)(x-1)(x−1)⋅x3+x(x−1)+1(x2+1)(x−1)

4−13+(−1)+1(2+1)(−1)

{\color{#c92786}{x^{4}-1x^{3}}}+x(x-1)+1(x^{2}+1)(x-1)x4−1x3+x(x−1)+1(x2+1)(x−1)

4

Distribute

4−3+(−1)+1(2+1)(−1)

x^{4}-x^{3}+{\color{#c92786}{x(x-1)}}+1(x^{2}+1)(x-1)x4−x3+x(x−1)+1(x2+1)(x−1)

4−3+2−+1(2+1)(−1)

x^{4}-x^{3}+{\color{#c92786}{x^{2}-x}}+1(x^{2}+1)(x-1)x4−x3+x2−x+1(x2+1)(x−1)

5

Multiply by 1

4−3+2−+1(2+1)(−1)

x^{4}-x^{3}+x^{2}-x+1(x^{2}+1)(x-1)x4−x3+x2−x+1(x2+1)(x−1)

4−3+2−+(2+1)(−1)

x^{4}-x^{3}+x^{2}-x+(x^{2}+1)(x-1)x4−x3+x2−x+(x2+1)(x−1)

6

Distribute

4−3+2−+(2+1)(−1)

x^{4}-x^{3}+x^{2}-x+{\color{#c92786}{(x^{2}+1)(x-1)}}x4−x3+x2−x+(x2+1)(x−1)

4−3+2−+(−1)⋅2+1(−1)

x^{4}-x^{3}+x^{2}-x+{\color{#c92786}{(x-1) \cdot x^{2}+1(x-1)}}x4