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

Question

Simplify the expression

x^{3} - 2 x^{2} - x

Evaluate

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

Multiply the terms

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

Expand the expression

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Calculate

x^{2} (x - 1)

Apply the distributive property

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

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

x^{3} - x^{2} \times 1

Any expression multiplied by 1 remains the same

x^{3} - x^{2}

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

Expand the expression

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Calculate

- x (x - 2)

Apply the distributive property

- x \times x - (- x \times 2)

Multiply the terms

- x^{2} - (- x \times 2)

Use the commutative property to reorder the terms

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

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

- x^{2} + 2 x

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

Subtract the terms

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Evaluate

- x^{2} - x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 1 - 1) x^{2}

Subtract the numbers

- 2 x^{2}

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

Solution

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Evaluate

2 x - 3 x

Collect like terms by calculating the sum or difference of their coefficients

(2 - 3) x

Subtract the numbers

- x

x^{3} - 2 x^{2} - x

Show Solution

Factor the expression

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

Evaluate

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

Multiply the terms

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

Simplify

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Evaluate

x^{2} (x - 1)

Apply the distributive property

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

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

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

Multiplying or dividing an odd number of negative terms equals a negative

x^{3} - x^{2}

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

Simplify

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Evaluate

- x (x - 2)

Apply the distributive property

- x \times x - x (- 2)

Multiply the terms

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

Use the commutative property to reorder the terms

- x^{2} + 2 x

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

Subtract the terms

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Evaluate

- x^{2} - x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 1 - 1) x^{2}

Subtract the numbers

- 2 x^{2}

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

Subtract the terms

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Evaluate

2 x - 3 x

Collect like terms by calculating the sum or difference of their coefficients

(2 - 3) x

Subtract the numbers

- x

x^{3} - 2 x^{2} - x

Rewrite the expression

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

Solution

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

Show Solution

Find the roots

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

Alternative Form

x_{1} \approx - 0.414214, x_{2} = 0, x_{3} \approx 2.414214

Evaluate

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

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

(x - 1) (x^{2}) - x (x - 2) - 3 x = 0

Calculate

(x - 1) x^{2} - x (x - 2) - 3 x = 0

Multiply the terms

x^{2} (x - 1) - x (x - 2) - 3 x = 0

Subtract the terms

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Simplify

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

Expand the expression

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Calculate

x^{2} (x - 1)

Apply the distributive property

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

Multiply the terms

x^{3} - x^{2} \times 1

Any expression multiplied by 1 remains the same

x^{3} - x^{2}

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

Expand the expression

More Steps

Calculate

- x (x - 2)

Apply the distributive property

- x \times x - (- x \times 2)

Multiply the terms

- x^{2} - (- x \times 2)

Use the commutative property to reorder the terms

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

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

- x^{2} + 2 x

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

Subtract the terms

More Steps

Evaluate

- x^{2} - x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 1 - 1) x^{2}

Subtract the numbers

- 2 x^{2}

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

x^{3} - 2 x^{2} + 2 x - 3 x = 0

Subtract the terms

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Simplify

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

Subtract the terms

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Evaluate

2 x - 3 x

Collect like terms by calculating the sum or difference of their coefficients

(2 - 3) x

Subtract the numbers

- x

x^{3} - 2 x^{2} - x

x^{3} - 2 x^{2} - x = 0

Factor the expression

x (x^{2} - 2 x - 1) = 0

Separate the equation into 2 possible cases

x = 0 x^{2} - 2 x - 1 = 0

Solve the equation

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Evaluate

x^{2} - 2 x - 1 = 0

Substitute a= 1,b= - 2 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 1 )}{2}

Simplify the expression

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Evaluate

(- 2)^{2} - 4 (- 1)

Simplify

(- 2)^{2} - (- 4)

Rewrite the expression

2^{2} - (- 4)

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

2^{2} + 4

Evaluate the power

4 + 4

Add the numbers

8

x = \frac{2 \pm 8}{2}

Simplify the radical expression

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Evaluate

8

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

The root of a product is equal to the product of the roots of each factor

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

x = \frac{2 \pm 2 2}{2}

Separate the equation into 2 possible cases

x = \frac{2 + 2 2}{2} x = \frac{2 - 2 2}{2}

Simplify the expression

x = 1 + 2 x = \frac{2 - 2 2}{2}

Simplify the expression

x = 1 + 2 x = 1 - 2

x = 0 x = 1 + 2 x = 1 - 2

Solution

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

Alternative Form

x_{1} \approx - 0.414214, x_{2} = 0, x_{3} \approx 2.414214

Show Solution