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

The solution to (2x-1)^3-(2x-1)^2-2(2x-1)-1 is 8x^3-16x^2+6x-1

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

simplify

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

8 x^{3} - 16 x^{2} + 6 x - 1

Solution steps

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

Expand

(2 x - 1)^{3} : 8 x^{3} - 12 x^{2} + 6 x - 1

= 8 x^{3} - 12 x^{2} + 6 x - 1 - (2 x - 1)^{2} - 2 (2 x - 1) - 1

Expand

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

= 8 x^{3} - 12 x^{2} + 6 x - 1 - 4 x^{2} + 4 x - 1 - 2 (2 x - 1) - 1

Expand

- 2 (2 x - 1) : - 4 x + 2

= 8 x^{3} - 12 x^{2} + 6 x - 1 - 4 x^{2} + 4 x - 1 - 4 x + 2 - 1

Group like terms

= 8 x^{3} - 12 x^{2} - 4 x^{2} + 6 x + 4 x - 4 x - 1 - 1 - 1 + 2

Add similar elements:

- 12 x^{2} - 4 x^{2} = - 16 x^{2}

= 8 x^{3} - 16 x^{2} + 6 x + 4 x - 4 x - 1 - 1 - 1 + 2

Add similar elements:

6 x + 4 x - 4 x = 6 x

= 8 x^{3} - 16 x^{2} + 6 x - 1 - 1 - 1 + 2

Add the numbers:

- 1 - 1 - 1 + 2 = - 1

= 8 x^{3} - 16 x^{2} + 6 x - 1

((((a^{2})^{2})^{3})^{2})^{2}

3 x - 9 y

x^{3} - x^{2} - x \cdot y^{2} + y^{2}

\frac{5 ( 2 x - 3 ) - 3 ( x + 4 )}{9}

\frac{2 cos ( x )}{sin ^{2} ( x )}

What is (2x-1)^3-(2x-1)^2-2(2x-1)-1 ?
The solution to (2x-1)^3-(2x-1)^2-2(2x-1)-1 is 8x^3-16x^2+6x-1