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

Question

Simplify the expression

12 x^{8} - 4 x^{4}

Evaluate

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

Multiply

More Steps

Multiply the terms

x^{3} \times 6 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 6

Add the numbers

x^{5} \times 6

Use the commutative property to reorder the terms

6 x^{5}

(6 x^{5} - 2 x \times 1) \times 2 x^{3}

Multiply the terms

(6 x^{5} - 2 x) \times 2 x^{3}

Multiply the terms

2 x^{3} (6 x^{5} - 2 x)

Apply the distributive property

2 x^{3} \times 6 x^{5} - 2 x^{3} \times 2 x

Multiply the terms

More Steps

Evaluate

2 x^{3} \times 6 x^{5}

Multiply the numbers

12 x^{3} \times x^{5}

Multiply the terms

More Steps

Evaluate

x^{3} \times x^{5}

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

x^{3 + 5}

Add the numbers

x^{8}

12 x^{8}

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

Solution

More Steps

Evaluate

2 x^{3} \times 2 x

Multiply the numbers

4 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}

4 x^{4}

12 x^{8} - 4 x^{4}

Show Solution

Factor the expression

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

Evaluate

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

Multiply

More Steps

Multiply the terms

x^{3} \times 6 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 6

Add the numbers

x^{5} \times 6

Use the commutative property to reorder the terms

6 x^{5}

(6 x^{5} - 2 x \times 1) \times 2 x^{3}

Multiply the terms

(6 x^{5} - 2 x) \times 2 x^{3}

Multiply the terms

2 x^{3} (6 x^{5} - 2 x)

Factor the expression

More Steps

Evaluate

6 x^{5} - 2 x

Rewrite the expression

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

Factor out 2 x from the expression

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

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

Solution

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

Show Solution

Find the roots

x_{1} = - \frac{4 27}{3}, x_{2} = 0, x_{3} = \frac{4 27}{3}

Alternative Form

x_{1} \approx - 0.759836, x_{2} = 0, x_{3} \approx 0.759836

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{3} \times 6 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 6

Add the numbers

x^{5} \times 6

Use the commutative property to reorder the terms

6 x^{5}

(6 x^{5} - 2 x \times 1) (2 x^{3}) = 0

Multiply the terms

(6 x^{5} - 2 x) (2 x^{3}) = 0

Multiply the terms

(6 x^{5} - 2 x) \times 2 x^{3} = 0

Multiply the terms

2 x^{3} (6 x^{5} - 2 x) = 0

Elimination the left coefficient

x^{3} (6 x^{5} - 2 x) = 0

Separate the equation into 2 possible cases

x^{3} = 0 6 x^{5} - 2 x = 0

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

x = 0 6 x^{5} - 2 x = 0

Solve the equation

More Steps

Evaluate

6 x^{5} - 2 x = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

x = 0 3 x^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

3 x^{4} - 1 = 0

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

3 x^{4} = 0 + 1

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

3 x^{4} = 1

Divide both sides

\frac{3 x ^{4}}{3} = \frac{1}{3}

Divide the numbers

x^{4} = \frac{1}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{1}{3}

Simplify the expression

x = \pm \frac{4 27}{3}

Separate the equation into 2 possible cases

x = \frac{4 27}{3} x = - \frac{4 27}{3}

x = 0 x = \frac{4 27}{3} x = - \frac{4 27}{3}

x = 0 x = 0 x = \frac{4 27}{3} x = - \frac{4 27}{3}

Find the union

x = 0 x = \frac{4 27}{3} x = - \frac{4 27}{3}

Solution

x_{1} = - \frac{4 27}{3}, x_{2} = 0, x_{3} = \frac{4 27}{3}

Alternative Form

x_{1} \approx - 0.759836, x_{2} = 0, x_{3} \approx 0.759836

Show Solution