Solve -x(x-3)*(-2x-8)

Question

Simplify the expression

2 x^{3} + 2 x^{2} - 24 x

Evaluate

- x (x - 3) (- 2 x - 8)

Multiply the terms

More Steps

Evaluate

- x (x - 3)

Apply the distributive property

- x \times x - (- x \times 3)

Multiply the terms

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

Use the commutative property to reorder the terms

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- x^{2} + 3 x

(- x^{2} + 3 x) (- 2 x - 8)

Apply the distributive property

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

Multiply the terms

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Evaluate

- x^{2} (- 2 x)

Multiply the numbers

2 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

2 x^{3}

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

Use the commutative property to reorder the terms

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

Multiply the terms

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Evaluate

3 x (- 2 x)

Multiply the numbers

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Evaluate

3 (- 2)

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

- 3 \times 2

Multiply the numbers

- 6

- 6 x \times x

Multiply the terms

- 6 x^{2}

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

Multiply the numbers

2 x^{3} - (- 8 x^{2}) - 6 x^{2} - 24 x

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x^{3} + 8 x^{2} - 6 x^{2} - 24 x

Solution

More Steps

Evaluate

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

Collect like terms by calculating the sum or difference of their coefficients

(8 - 6) x^{2}

Subtract the numbers

2 x^{2}

2 x^{3} + 2 x^{2} - 24 x

Show Solution

Factor the expression

2 x (x - 3) (x + 4)

Evaluate

- x (x - 3) (- 2 x - 8)

Factor the expression

- x (x - 3) (- 2) (x + 4)

Solution

2 x (x - 3) (x + 4)

Show Solution

Find the roots

x_{1} = - 4, x_{2} = 0, x_{3} = 3

Evaluate

- x (x - 3) (- 2 x - 8)

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

- x (x - 3) (- 2 x - 8) = 0

Change the sign

x (x - 3) (- 2 x - 8) = 0

Separate the equation into 3 possible cases

x = 0 x - 3 = 0 - 2 x - 8 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3 - 2 x - 8 = 0

Solve the equation

More Steps

Evaluate

- 2 x - 8 = 0

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

- 2 x = 0 + 8

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

- 2 x = 8

Change the signs on both sides of the equation

2 x = - 8

Divide both sides

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

Divide the numbers

x = \frac{- 8}{2}

Divide the numbers

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Evaluate

\frac{- 8}{2}

Reduce the numbers

\frac{- 4}{1}

Calculate

- 4

x = - 4

x = 0 x = 3 x = - 4

Solution

x_{1} = - 4, x_{2} = 0, x_{3} = 3

Show Solution