Solve (-3x-1)(2x^2 8x 1)

Question

Simplify the expression

- 48 x^{4} - 16 x^{3}

Evaluate

(- 3 x - 1) (2 x^{2} \times 8 x \times 1)

Remove the parentheses

(- 3 x - 1) \times 2 x^{2} \times 8 x \times 1

Rewrite the expression

(- 3 x - 1) \times 2 x^{2} \times 8 x

Multiply the terms

(- 3 x - 1) \times 16 x^{2} \times x

Multiply the terms with the same base by adding their exponents

(- 3 x - 1) \times 16 x^{2 + 1}

Add the numbers

(- 3 x - 1) \times 16 x^{3}

Multiply the terms

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

Apply the distributive property

16 x^{3} (- 3 x) - 16 x^{3} \times 1

Multiply the terms

More Steps

Evaluate

16 x^{3} (- 3 x)

Multiply the numbers

More Steps

Evaluate

16 (- 3)

Multiplying or dividing an odd number of negative terms equals a negative

- 16 \times 3

Multiply the numbers

- 48

- 48 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}

- 48 x^{4}

- 48 x^{4} - 16 x^{3} \times 1

Solution

- 48 x^{4} - 16 x^{3}

Show Solution

Find the roots

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0

Evaluate

(- 3 x - 1) (2 x^{2} \times 8 x \times 1)

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

(- 3 x - 1) (2 x^{2} \times 8 x \times 1) = 0

Multiply the terms

More Steps

Multiply the terms

2 x^{2} \times 8 x \times 1

Rewrite the expression

2 x^{2} \times 8 x

Multiply the terms

16 x^{2} \times x

Multiply the terms with the same base by adding their exponents

16 x^{2 + 1}

Add the numbers

16 x^{3}

(- 3 x - 1) \times 16 x^{3} = 0

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 - 3 x - 1 = 0

Solve the equation

More Steps

Evaluate

- 3 x - 1 = 0

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

- 3 x = 0 + 1

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

- 3 x = 1

Change the signs on both sides of the equation

3 x = - 1

Divide both sides

\frac{3 x}{3} = \frac{- 1}{3}

Divide the numbers

x = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{3}

x = 0 x = - \frac{1}{3}

Solution

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

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0

Show Solution