Solve (-4x^24x) (-6x^2 -8)

Question

Simplify the expression

96 x^{5} + 128 x^{3}

Evaluate

(- 4 x^{2} \times 4 x) (- 6 x^{2} - 8)

Remove the parentheses

- 4 x^{2} \times 4 x (- 6 x^{2} - 8)

Multiply the terms

- 16 x^{2} \times x (- 6 x^{2} - 8)

Multiply the terms with the same base by adding their exponents

- 16 x^{2 + 1} (- 6 x^{2} - 8)

Add the numbers

- 16 x^{3} (- 6 x^{2} - 8)

Apply the distributive property

- 16 x^{3} (- 6 x^{2}) - (- 16 x^{3} \times 8)

Multiply the terms

More Steps

Evaluate

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

Multiply the numbers

More Steps

Evaluate

- 16 (- 6)

Multiplying or dividing an even number of negative terms equals a positive

16 \times 6

Multiply the numbers

96

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

Multiply the terms

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Evaluate

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

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

x^{3 + 2}

Add the numbers

x^{5}

96 x^{5}

96 x^{5} - (- 16 x^{3} \times 8)

Multiply the numbers

96 x^{5} - (- 128 x^{3})

Solution

96 x^{5} + 128 x^{3}

Show Solution

Factor the expression

32 x^{3} (3 x^{2} + 4)

Evaluate

(- 4 x^{2} \times 4 x) (- 6 x^{2} - 8)

Remove the parentheses

- 4 x^{2} \times 4 x (- 6 x^{2} - 8)

Multiply

More Steps

Evaluate

- 4 x^{2} \times 4 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}

- 16 x^{3} (- 6 x^{2} - 8)

Factor the expression

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

Solution

32 x^{3} (3 x^{2} + 4)

Show Solution

Find the roots

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

Alternative Form

x_{1} \approx - 1.154701 i, x_{2} \approx 1.154701 i, x_{3} = 0

Evaluate

(- 4 x^{2} \times 4 x) (- 6 x^{2} - 8)

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

(- 4 x^{2} \times 4 x) (- 6 x^{2} - 8) = 0

Multiply

More Steps

Multiply the terms

- 4 x^{2} \times 4 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}

(- 16 x^{3}) (- 6 x^{2} - 8) = 0

Remove the parentheses

- 16 x^{3} (- 6 x^{2} - 8) = 0

Change the sign

16 x^{3} (- 6 x^{2} - 8) = 0

Elimination the left coefficient

x^{3} (- 6 x^{2} - 8) = 0

Separate the equation into 2 possible cases

x^{3} = 0 - 6 x^{2} - 8 = 0

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

x = 0 - 6 x^{2} - 8 = 0

Solve the equation

More Steps

Evaluate

- 6 x^{2} - 8 = 0

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

- 6 x^{2} = 0 + 8

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

- 6 x^{2} = 8

Change the signs on both sides of the equation

6 x^{2} = - 8

Divide both sides

\frac{6 x ^{2}}{6} = \frac{- 8}{6}

Divide the numbers

x^{2} = \frac{- 8}{6}

Divide the numbers

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Evaluate

\frac{- 8}{6}

Cancel out the common factor 2

\frac{- 4}{3}

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

- \frac{4}{3}

x^{2} = - \frac{4}{3}

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

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

Simplify the expression

More Steps

Evaluate

- \frac{4}{3}

Evaluate the power

\frac{4}{3} \times - 1

Evaluate the power

\frac{4}{3} \times i

Evaluate the power

\frac{2 3}{3} i

x = \pm \frac{2 3}{3} i

Separate the equation into 2 possible cases

x = \frac{2 3}{3} i x = - \frac{2 3}{3} i

x = 0 x = \frac{2 3}{3} i x = - \frac{2 3}{3} i

Solution

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

Alternative Form

x_{1} \approx - 1.154701 i, x_{2} \approx 1.154701 i, x_{3} = 0

Show Solution