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

The solution to (x-1)(x+1)-3x(x^2-2x-1) is -3x^3+7x^2+3x-1

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

simplify

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

- 3 x^{3} + 7 x^{2} + 3 x - 1

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

x^{2} + 6 x^{2} = 7 x^{2}

= - 3 x^{3} + 7 x^{2} + 3 x - 1

\frac{1}{2} \div \frac{3}{8}

9 + 5 r - 9 r

(- 2 + i)^{3}

- 7 + (- 7)

- 7 + (- 6)

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