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

Question

Simplify the expression

x^{6} - x^{5}

Evaluate

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

Multiply the exponents

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

Multiply the numbers

x (x - 1) x^{4}

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{5} (x - 1)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

x^{6} - x^{5} \times 1

Solution

x^{6} - x^{5}

Show Solution

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

Evaluate

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

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

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

Evaluate the power

More Steps

Evaluate

(x^{2})^{2}

Transform the expression

x^{2 \times 2}

Multiply the numbers

x^{4}

x (x - 1) x^{4} = 0

Multiply

More Steps

Multiply the terms

x (x - 1) x^{4}

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{5} (x - 1)

x^{5} (x - 1) = 0

Separate the equation into 2 possible cases

x^{5} = 0 x - 1 = 0

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

x = 0 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 = 0 x = 1

Solution

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

Show Solution