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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Distribute parentheses

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

Simplify

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

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

(- 32)^{- \frac{4}{5}}

\frac{18}{25}

\frac{3}{8} \cdot \frac{3}{5}

(6 x + 5) (2 x - 1)

\frac{28}{7} \div \frac{4}{5}

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