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

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

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

expand

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

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

Solution steps

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

Distribute parentheses

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

Simplify

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

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

- 10 \times (- 2)

8 - 6 x + 2 x^{2}

\frac{3}{7 + 2}

i^{343}

\frac{67}{4}

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