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

Question

Simplify the expression

x^{8} - x^{7}

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{6} \times x (x - 1)

Multiply the terms with the same base by adding their exponents

x^{1 + 6} (x - 1)

Add the numbers

x^{7} (x - 1)

Apply the distributive property

x^{7} \times x - x^{7} \times 1

Multiply the terms

More Steps

Evaluate

x^{7} \times x

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

x^{7 + 1}

Add the numbers

x^{8}

x^{8} - x^{7} \times 1

Solution

x^{8} - x^{7}

Show Solution

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

Evaluate

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

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

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

Any expression multiplied by 1 remains the same

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

Calculate

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

Calculate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{6} \times x (x - 1)

Multiply the terms with the same base by adding their exponents

x^{1 + 6} (x - 1)

Add the numbers

x^{7} (x - 1)

x^{7} (x - 1) = 0

Separate the equation into 2 possible cases

x^{7} = 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