Solve (x-1)(3x^3 4x)

Question

Simplify the expression

12 x^{5} - 12 x^{4}

Evaluate

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

Remove the parentheses

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

Multiply the terms

(x - 1) \times 12 x^{3} \times x

Multiply the terms with the same base by adding their exponents

(x - 1) \times 12 x^{3 + 1}

Add the numbers

(x - 1) \times 12 x^{4}

Multiply the terms

12 x^{4} (x - 1)

Apply the distributive property

12 x^{4} \times x - 12 x^{4} \times 1

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}

12 x^{5} - 12 x^{4} \times 1

Solution

12 x^{5} - 12 x^{4}

Show Solution

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

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 x^{3} \times 4 x

Multiply the terms

12 x^{3} \times x

Multiply the terms with the same base by adding their exponents

12 x^{3 + 1}

Add the numbers

12 x^{4}

(x - 1) \times 12 x^{4} = 0

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

x^{4} = 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