What is (x-1)^3-(x-3)(x^2+3x+9)-3x(1-x) ?

The solution to (x-1)^3-(x-3)(x^2+3x+9)-3x(1-x) is 26

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simplify (x-1)^3-(x-3)(x^2+3x+9)-3x(1-x)

simplify

(x - 1)^{3} - (x - 3) (x^{2} + 3 x + 9) - 3 x (1 - x)

26

Solution steps

(x - 1)^{3} - (x - 3) (x^{2} + 3 x + 9) - 3 x (1 - x)

Expand

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

= x^{3} - 3 x^{2} + 3 x - 1 - (x - 3) (x^{2} + 3 x + 9) - 3 x (1 - x)

Expand

- (x - 3) (x^{2} + 3 x + 9) : - x^{3} + 27

= x^{3} - 3 x^{2} + 3 x - 1 - x^{3} + 27 - 3 x (1 - x)

Expand

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

= x^{3} - 3 x^{2} + 3 x - 1 - x^{3} + 27 - 3 x + 3 x^{2}

Group like terms

= x^{3} - x^{3} - 3 x^{2} + 3 x^{2} + 3 x - 3 x - 1 + 27

Add similar elements:

x^{3} - x^{3} = 0

= - 3 x^{2} + 3 x^{2} + 3 x - 3 x - 1 + 27

Add similar elements:

- 3 x^{2} + 3 x^{2} = 0

= 3 x - 3 x - 1 + 27

Add similar elements:

3 x - 3 x = 0

= - 1 + 27

Add the numbers:

- 1 + 27 = 26

= 26

1 (x^{4})^{2} \cdot (x^{4})^{- 2}

3 (4 x + 5)^{3}

(3 x^{5} + y^{5}) 2

r^{\frac{- 3}{2}}

(x - 2 y)^{2} - 25

What is (x-1)^3-(x-3)(x^2+3x+9)-3x(1-x) ?
The solution to (x-1)^3-(x-3)(x^2+3x+9)-3x(1-x) is 26