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

Question

Simplify the expression

x^{10} - x^{9}

Evaluate

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

Multiply the exponents

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

Any expression multiplied by 1 remains the same

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

Multiply the numbers

x^{4} \times x^{3} (x - 1) x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 3 + 2} (x - 1)

Add the numbers

x^{9} (x - 1)

Apply the distributive property

x^{9} \times x - x^{9} \times 1

Multiply the terms

More Steps

Evaluate

x^{9} \times x

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

x^{9 + 1}

Add the numbers

x^{10}

x^{10} - x^{9} \times 1

Solution

x^{10} - x^{9}

Show Solution

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

Evaluate

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

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

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

Any expression multiplied by 1 remains the same

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

Calculate

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

Evaluate the power

More Steps

Evaluate

(x^{2})^{2}

Transform the expression

x^{2 \times 2}

Multiply the numbers

x^{4}

x^{4} \times x^{3} (x - 1) x^{2} = 0

Multiply

More Steps

Multiply the terms

x^{4} \times x^{3} (x - 1) x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 3 + 2} (x - 1)

Add the numbers

x^{9} (x - 1)

x^{9} (x - 1) = 0

Separate the equation into 2 possible cases

x^{9} = 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