What is expand (x+1)(x^2+1+x)(x^2+1-x) ?

The solution to expand (x+1)(x^2+1+x)(x^2+1-x) is x^5+x^4+x^3+x^2+x+1

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expand (x+1)(x^2+1+x)(x^2+1-x)

expand

(x + 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

x^{5} + x^{4} + x^{3} + x^{2} + x + 1

Solution steps

(x + 1) (x^{2} + 1 + x) (x^{2} + 1 - x)

Expand

(x + 1) (x^{2} + 1 + x) : x^{3} + 2 x^{2} + 2 x + 1

= (x^{3} + 2 x^{2} + 2 x + 1) (x^{2} + 1 - x)

Distribute parentheses

= x^{3} x^{2} + x^{3} \cdot 1 + x^{3} (- x) + 2 x^{2} x^{2} + 2 x^{2} \cdot 1 + 2 x^{2} (- x) + 2 x x^{2} + 2 x \cdot 1 + 2 x (- x) + 1 \cdot x^{2} + 1 \cdot 1 + 1 \cdot (- x)

Simplify

x^{3} x^{2} + x^{3} \cdot 1 + x^{3} (- x) + 2 x^{2} x^{2} + 2 x^{2} \cdot 1 + 2 x^{2} (- x) + 2 x x^{2} + 2 x \cdot 1 + 2 x (- x) + 1 \cdot x^{2} + 1 \cdot 1 + 1 \cdot (- x) : x^{5} + x^{4} + x^{3} + x^{2} + x + 1

= x^{5} + x^{4} + x^{3} + x^{2} + x + 1

x^{5} \cdot x^{6}

x^{5} \cdot x^{8}

3 (8 - 2 x) + 2 (7 x - 19)

(9 - 2 i) - (- 3 - 2 i)

What is expand (x+1)(x^2+1+x)(x^2+1-x) ?
The solution to expand (x+1)(x^2+1+x)(x^2+1-x) is x^5+x^4+x^3+x^2+x+1