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

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

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

3 x + 2 x = 5 x

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

Subtract the numbers:

- 1 - 1 = - 2

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

9 x^{0}

3 - 33

ln (1 - 1)

e^{3 l n ∣ x ∣}

2 lo g_{4} (8)