Solve -1/2(x^2)*(x 1)^3*(x-1)^2*(x-2)

Question

Simplify the expression

- \frac{1}{2} x^{8} + 2 x^{7} - \frac{5}{2} x^{6} + x^{5}

Evaluate

- \frac{1}{2} x^{2} (x \times 1)^{3} (x - 1)^{2} (x - 2)

Any expression multiplied by 1 remains the same

- \frac{1}{2} x^{2} \times x^{3} (x - 1)^{2} (x - 2)

Multiply the terms

More Steps

- (\frac{1}{2} x - 1) x^{5} (x - 1)^{2}

Calculate

(- \frac{1}{2} x + 1) x^{5} (x - 1)^{2}

Expand the expression

More Steps

(- \frac{1}{2} x + 1) x^{5} (x^{2} - 2 x + 1)

Multiply the terms

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(- \frac{1}{2} x^{6} + x^{5}) (x^{2} - 2 x + 1)

Apply the distributive property

- \frac{1}{2} x^{6} \times x^{2} - (- \frac{1}{2} x^{6} \times 2 x) - \frac{1}{2} x^{6} \times 1 + x^{5} \times x^{2} - x^{5} \times 2 x + x^{5} \times 1

Multiply the terms

More Steps

- \frac{1}{2} x^{8} - (- \frac{1}{2} x^{6} \times 2 x) - \frac{1}{2} x^{6} \times 1 + x^{5} \times x^{2} - x^{5} \times 2 x + x^{5} \times 1

Multiply the terms

More Steps

- \frac{1}{2} x^{8} - (- x^{7}) - \frac{1}{2} x^{6} \times 1 + x^{5} \times x^{2} - x^{5} \times 2 x + x^{5} \times 1

Any expression multiplied by 1 remains the same

- \frac{1}{2} x^{8} - (- x^{7}) - \frac{1}{2} x^{6} + x^{5} \times x^{2} - x^{5} \times 2 x + x^{5} \times 1

Multiply the terms

More Steps

- \frac{1}{2} x^{8} - (- x^{7}) - \frac{1}{2} x^{6} + x^{7} - x^{5} \times 2 x + x^{5} \times 1

Multiply the terms

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- \frac{1}{2} x^{8} - (- x^{7}) - \frac{1}{2} x^{6} + x^{7} - 2 x^{6} + x^{5} \times 1

Any expression multiplied by 1 remains the same

- \frac{1}{2} x^{8} - (- x^{7}) - \frac{1}{2} x^{6} + x^{7} - 2 x^{6} + x^{5}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- \frac{1}{2} x^{8} + x^{7} - \frac{1}{2} x^{6} + x^{7} - 2 x^{6} + x^{5}

Add the terms

More Steps

- \frac{1}{2} x^{8} + 2 x^{7} - \frac{1}{2} x^{6} - 2 x^{6} + x^{5}

Solution

More Steps

- \frac{1}{2} x^{8} + 2 x^{7} - \frac{5}{2} x^{6} + x^{5}

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Find the roots

x_{1} = 0, x_{2} = 1, x_{3} = 2

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