Solve (x-1)(x^2)(x^3)(x^6)

Question

Simplify the expression

x^{12} - x^{11}

Evaluate

(x - 1) x^{2} \times x^{3} \times x^{6}

Multiply the terms with the same base by adding their exponents

(x - 1) x^{2 + 3 + 6}

Add the numbers

(x - 1) x^{11}

Multiply the terms

x^{11} (x - 1)

Apply the distributive property

x^{11} \times x - x^{11} \times 1

Multiply the terms

More Steps

Evaluate

x^{11} \times x

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

x^{11 + 1}

Add the numbers

x^{12}

x^{12} - x^{11} \times 1

Solution

x^{12} - x^{11}

Show Solution

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

Evaluate

(x - 1) (x^{2}) (x^{3}) (x^{6})

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

(x - 1) (x^{2}) (x^{3}) (x^{6}) = 0

Calculate

(x - 1) x^{2} (x^{3}) (x^{6}) = 0

Calculate

(x - 1) x^{2} \times x^{3} (x^{6}) = 0

Calculate

(x - 1) x^{2} \times x^{3} \times x^{6} = 0

Multiply the terms

More Steps

Multiply the terms

(x - 1) x^{2} \times x^{3} \times x^{6}

Multiply the terms with the same base by adding their exponents

(x - 1) x^{2 + 3 + 6}

Add the numbers

(x - 1) x^{11}

Multiply the terms

x^{11} (x - 1)

x^{11} (x - 1) = 0

Separate the equation into 2 possible cases

x^{11} = 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