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

Question

Simplify the expression

x^{4} - 2 x^{2} - x^{3} + 2 x

Evaluate

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

Remove the parentheses

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Evaluate

x (x - 1)

Apply the distributive property

x \times x - x \times 1

Multiply the terms

x^{2} - x \times 1

Any expression multiplied by 1 remains the same

x^{2} - x

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

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

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

x^{2 + 2}

Add the numbers

x^{4}

x^{4} - x^{2} \times 2 - x \times x^{2} - (- x \times 2)

Use the commutative property to reorder the terms

x^{4} - 2 x^{2} - x \times x^{2} - (- x \times 2)

Multiply the terms

More Steps

Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

x^{4} - 2 x^{2} - x^{3} - (- x \times 2)

Use the commutative property to reorder the terms

x^{4} - 2 x^{2} - x^{3} - (- 2 x)

Solution

x^{4} - 2 x^{2} - x^{3} + 2 x

Show Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 1, x_{4} = 2

Alternative Form

x_{1} \approx - 1.414214, x_{2} = 0, x_{3} = 1, x_{4} \approx 1.414214

Evaluate

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

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

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

Any expression multiplied by 1 remains the same

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

Separate the equation into 3 possible cases

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

Solve the equation

More Steps

Evaluate

x^{2} - 2 = 0

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

x^{2} = 0 + 2

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

x^{2} = 2

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 2

Separate the equation into 2 possible cases

x = 2 x = - 2

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

Solution

x_{1} = - 2, x_{2} = 0, x_{3} = 1, x_{4} = 2

Alternative Form

x_{1} \approx - 1.414214, x_{2} = 0, x_{3} = 1, x_{4} \approx 1.414214

Show Solution