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

The solution to (-x^2+x-1)^3+|x^2-x+1| is -x^6+3x^5-6x^4+7x^3-6x^2+3x-1+|x^2-x+1|

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simplify (-x^2+x-1)^3+|x^2-x+1|

simplify

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

- x^{6} + 3 x^{5} - 6 x^{4} + 7 x^{3} - 6 x^{2} + 3 x - 1 + x^{2} - x + 1

Solution steps

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

Simplify

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

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

Expand

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

= (x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1) (- x^{2} + x - 1) + x^{2} - x + 1

Distribute parentheses

= x^{4} (- x^{2}) + x^{4} x + x^{4} (- 1) - 2 x^{3} (- x^{2}) - 2 x^{3} x - 2 x^{3} (- 1) + 3 x^{2} (- x^{2}) + 3 x^{2} x + 3 x^{2} (- 1) - 2 x (- x^{2}) - 2 xx - 2 x (- 1) + 1 \cdot (- x^{2}) + 1 \cdot x + 1 \cdot (- 1) + x^{2} - x + 1

Simplify

x^{4} (- x^{2}) + x^{4} x + x^{4} (- 1) - 2 x^{3} (- x^{2}) - 2 x^{3} x - 2 x^{3} (- 1) + 3 x^{2} (- x^{2}) + 3 x^{2} x + 3 x^{2} (- 1) - 2 x (- x^{2}) - 2 xx - 2 x (- 1) + 1 \cdot (- x^{2}) + 1 \cdot x + 1 \cdot (- 1) : - x^{6} + 3 x^{5} - 6 x^{4} + 7 x^{3} - 6 x^{2} + 3 x - 1

= - x^{6} + 3 x^{5} - 6 x^{4} + 7 x^{3} - 6 x^{2} + 3 x - 1 + x^{2} - x + 1

5 x^{10} \cdot y^{5} + 10 x^{8} \cdot y^{15} + 25 x^{16} \cdot y^{25}

9 m^{4} + 14 m^{2} \cdot n^{2} + 25 n^{4}

(4 x + 2) (3 x + 2)

- sin^{2} (x) - cos^{2} (x) + sin (x)

\frac{2}{( x - \frac{1}{x} )} - \frac{( \frac{1}{x} )}{( 1 - \frac{1}{x} )}

What is (-x^2+x-1)^3+|x^2-x+1| ?
The solution to (-x^2+x-1)^3+|x^2-x+1| is -x^6+3x^5-6x^4+7x^3-6x^2+3x-1+|x^2-x+1|