Solve (x^(3)-1)(x-1)

Question

Simplify the expression

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

Evaluate

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

Apply the distributive property

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

Multiply the terms

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Evaluate

x^{3} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 1}

Add the numbers

x^{4}

x^{4} - x^{3} \times 1 - x - (- 1)

Any expression multiplied by 1 remains the same

x^{4} - x^{3} - x - (- 1)

Solution

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

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

Evaluate

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

Factor the expression

More Steps

Evaluate

x^{3} - 1

Calculate

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

Rewrite the expression

x \times x^{2} + x \times x + x - x^{2} - x - 1

Factor out x from the expression

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

Factor out - 1 from the expression

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

Factor out x^{2} + x + 1 from the expression

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

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

Solution

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

Show Solution

x = 1

Evaluate

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

To find the roots of the expression,set the expression equal to 0

(x^{3} - 1) (x - 1) = 0

Separate the equation into 2 possible cases

x^{3} - 1 = 0 x - 1 = 0

Solve the equation

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Evaluate

x^{3} - 1 = 0

Move the constant to the right-hand side and change its sign

x^{3} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x^{3} = 1

Take the 3 -th root on both sides of the equation

3 x^{3} = 31

Calculate

x = 31

Simplify the root

x = 1

x = 1 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x = 1

x = 1 x = 1

Solution

x = 1

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