What is expand (x^3-x+1)(x^2-1)(2x-1) ?

The solution to expand (x^3-x+1)(x^2-1)(2x-1) is 2x^6-x^5-4x^4+4x^3+x^2-3x+1

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expand (x^3-x+1)(x^2-1)(2x-1)

expand

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

2 x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + x^{2} - 3 x + 1

Solution steps

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

Expand

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

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

Distribute parentheses

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

Simplify

x^{3} \cdot 2 x^{3} + x^{3} (- x^{2}) + x^{3} (- 2 x) + x^{3} \cdot 1 - x \cdot 2 x^{3} - x (- x^{2}) - x (- 2 x) - x \cdot 1 + 1 \cdot 2 x^{3} + 1 \cdot (- x^{2}) + 1 \cdot (- 2 x) + 1 \cdot 1 : 2 x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + x^{2} - 3 x + 1

= 2 x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + x^{2} - 3 x + 1

125 x^{3} - 343 y^{3}

\frac{5 x + 10}{10}

a^{- 1} + b^{- 1}

(\frac{2}{3 \cdot a ^{6} \cdot b ^{4} \cdot c ^{- 3} + 11 a \cdot b ^{2}})^{2}

6 \cdot y^{- 2}

What is expand (x^3-x+1)(x^2-1)(2x-1) ?
The solution to expand (x^3-x+1)(x^2-1)(2x-1) is 2x^6-x^5-4x^4+4x^3+x^2-3x+1