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

Question

Simplify the expression

x^{5} - 2 x^{4}

Evaluate

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

Remove the parentheses

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

Rewrite the expression

x^{3} (x - 2) x

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{4} (x - 2)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

x^{5} - x^{4} \times 2

Solution

x^{5} - 2 x^{4}

Show Solution

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

Evaluate

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

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

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

Calculate

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

Any expression multiplied by 1 remains the same

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

Multiply

More Steps

Multiply the terms

x^{3} (x - 2) x

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{4} (x - 2)

x^{4} (x - 2) = 0

Separate the equation into 2 possible cases

x^{4} = 0 x - 2 = 0

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

x = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 2

Solution

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

Show Solution