Solve x(4x-4)(2x^2)

Question

Simplify the expression

8 x^{4} - 8 x^{3}

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

Apply the distributive property

2 x^{3} \times 4 x - 2 x^{3} \times 4

Multiply the terms

More Steps

Evaluate

2 x^{3} \times 4 x

Multiply the numbers

8 x^{3} \times x

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

8 x^{4}

8 x^{4} - 2 x^{3} \times 4

Solution

8 x^{4} - 8 x^{3}

Show Solution

Factor the expression

8 x^{3} (x - 1)

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

Factor the expression

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

Solution

8 x^{3} (x - 1)

Show Solution

Find the roots

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

Evaluate

x (4 x - 4) (2 x^{2})

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

x (4 x - 4) (2 x^{2}) = 0

Multiply the terms

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

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

Elimination the left coefficient

x^{3} (4 x - 4) = 0

Separate the equation into 2 possible cases

x^{3} = 0 4 x - 4 = 0

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

x = 0 4 x - 4 = 0

Solve the equation

More Steps

Evaluate

4 x - 4 = 0

Move the constant to the right-hand side and change its sign

4 x = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

4 x = 4

Divide both sides

\frac{4 x}{4} = \frac{4}{4}

Divide the numbers

x = \frac{4}{4}

Divide the numbers

More Steps

Evaluate

\frac{4}{4}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

x = 0 x = 1

Solution

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

Show Solution