Solve -4d(2d^2-1)

Question

Simplify the expression

- 8 d^{3} + 4 d

Evaluate

- 4 d (2 d^{2} - 1)

Apply the distributive property

- 4 d \times 2 d^{2} - (- 4 d \times 1)

Multiply the terms

More Steps

Evaluate

- 4 d \times 2 d^{2}

Multiply the numbers

- 8 d \times d^{2}

Multiply the terms

More Steps

Evaluate

d \times d^{2}

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

d^{1 + 2}

Add the numbers

d^{3}

- 8 d^{3}

- 8 d^{3} - (- 4 d \times 1)

Any expression multiplied by 1 remains the same

- 8 d^{3} - (- 4 d)

Solution

- 8 d^{3} + 4 d

Show Solution

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

Alternative Form

d_{1} \approx - 0.707107, d_{2} = 0, d_{3} \approx 0.707107

Evaluate

- 4 d (2 d^{2} - 1)

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

- 4 d (2 d^{2} - 1) = 0

Change the sign

4 d (2 d^{2} - 1) = 0

Elimination the left coefficient

d (2 d^{2} - 1) = 0

Separate the equation into 2 possible cases

d = 0 2 d^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

2 d^{2} - 1 = 0

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

2 d^{2} = 0 + 1

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

2 d^{2} = 1

Divide both sides

\frac{2 d ^{2}}{2} = \frac{1}{2}

Divide the numbers

d^{2} = \frac{1}{2}

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

d = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

d = \pm \frac{2}{2}

Separate the equation into 2 possible cases

d = \frac{2}{2} d = - \frac{2}{2}

d = 0 d = \frac{2}{2} d = - \frac{2}{2}

Solution

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

Alternative Form

d_{1} \approx - 0.707107, d_{2} = 0, d_{3} \approx 0.707107

Show Solution