Solve (x^2-1 ) ( x^22x )

Question

Simplify the expression

2 x^{5} - 2 x^{3}

Evaluate

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

Remove the parentheses

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

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

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

x^{3 + 2}

Add the numbers

x^{5}

2 x^{5} - 2 x^{3} \times 1

Solution

2 x^{5} - 2 x^{3}

Show Solution

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

Evaluate

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

Remove the parentheses

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

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

Multiply the terms

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

Solution

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

Show Solution

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

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

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

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

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

Solve the equation

More Steps

Evaluate

x^{2} - 1 = 0

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

x^{2} = 0 + 1

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

x^{2} = 1

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

x = \pm 1

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

x = 0 x = 1 x = - 1

Solution

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

Show Solution