Solve (2h-4)(-h^2-h-4)

Question

Simplify the expression

- 2 h^{3} + 2 h^{2} - 4 h + 16

Evaluate

(2 h - 4) (- h^{2} - h - 4)

Apply the distributive property

2 h (- h^{2}) - 2 h \times h - 2 h \times 4 - 4 (- h^{2}) - (- 4 h) - (- 4 \times 4)

Multiply the terms

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Evaluate

2 h (- h^{2})

Multiply the numbers

- 2 h \times h^{2}

Multiply the terms

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Evaluate

h \times h^{2}

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

h^{1 + 2}

Add the numbers

h^{3}

- 2 h^{3}

- 2 h^{3} - 2 h \times h - 2 h \times 4 - 4 (- h^{2}) - (- 4 h) - (- 4 \times 4)

Multiply the terms

- 2 h^{3} - 2 h^{2} - 2 h \times 4 - 4 (- h^{2}) - (- 4 h) - (- 4 \times 4)

Multiply the numbers

- 2 h^{3} - 2 h^{2} - 8 h - 4 (- h^{2}) - (- 4 h) - (- 4 \times 4)

Multiply the numbers

- 2 h^{3} - 2 h^{2} - 8 h + 4 h^{2} - (- 4 h) - (- 4 \times 4)

Multiply the numbers

- 2 h^{3} - 2 h^{2} - 8 h + 4 h^{2} - (- 4 h) - (- 16)

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 h^{3} - 2 h^{2} - 8 h + 4 h^{2} + 4 h + 16

Add the terms

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Evaluate

- 2 h^{2} + 4 h^{2}

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

(- 2 + 4) h^{2}

Add the numbers

2 h^{2}

- 2 h^{3} + 2 h^{2} - 8 h + 4 h + 16

Solution

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Evaluate

- 8 h + 4 h

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

(- 8 + 4) h

Add the numbers

- 4 h

- 2 h^{3} + 2 h^{2} - 4 h + 16

Show Solution

Factor the expression

- 2 (h - 2) (h^{2} + h + 4)

Evaluate

(2 h - 4) (- h^{2} - h - 4)

Factor the expression

2 (h - 2) (- h^{2} - h - 4)

Factor the expression

2 (h - 2) (- 1) (h^{2} + h + 4)

Solution

- 2 (h - 2) (h^{2} + h + 4)

Show Solution

Find the roots

h_{1} = - \frac{1}{2} - \frac{15}{2} i, h_{2} = - \frac{1}{2} + \frac{15}{2} i, h_{3} = 2

Alternative Form

h_{1} \approx - 0.5 - 1.936492 i, h_{2} \approx - 0.5 + 1.936492 i, h_{3} = 2

Evaluate

(2 h - 4) (- h^{2} - h - 4)

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

(2 h - 4) (- h^{2} - h - 4) = 0

Separate the equation into 2 possible cases

2 h - 4 = 0 - h^{2} - h - 4 = 0

Solve the equation

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Evaluate

2 h - 4 = 0

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

2 h = 0 + 4

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

2 h = 4

Divide both sides

\frac{2 h}{2} = \frac{4}{2}

Divide the numbers

h = \frac{4}{2}

Divide the numbers

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Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

h = 2

h = 2 - h^{2} - h - 4 = 0

Solve the equation

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Evaluate

- h^{2} - h - 4 = 0

Multiply both sides

h^{2} + h + 4 = 0

Substitute a= 1,b= 1 and c= 4 into the quadratic formula h = \frac{- b \pm b ^{2} - 4 a c}{2 a}

h = \frac{- 1 \pm 1 ^{2} - 4 \times 4}{2}

Simplify the expression

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Evaluate

1^{2} - 4 \times 4

1 raised to any power equals to 1

1 - 4 \times 4

Multiply the numbers

1 - 16

Subtract the numbers

- 15

h = \frac{- 1 \pm - 15}{2}

Simplify the radical expression

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Evaluate

- 15

Evaluate the power

15 \times - 1

Evaluate the power

15 \times i

h = \frac{- 1 \pm 15 \times i}{2}

Separate the equation into 2 possible cases

h = \frac{- 1 + 15 \times i}{2} h = \frac{- 1 - 15 \times i}{2}

Simplify the expression

h = - \frac{1}{2} + \frac{15}{2} i h = \frac{- 1 - 15 \times i}{2}

Simplify the expression

h = - \frac{1}{2} + \frac{15}{2} i h = - \frac{1}{2} - \frac{15}{2} i

h = 2 h = - \frac{1}{2} + \frac{15}{2} i h = - \frac{1}{2} - \frac{15}{2} i

Solution

h_{1} = - \frac{1}{2} - \frac{15}{2} i, h_{2} = - \frac{1}{2} + \frac{15}{2} i, h_{3} = 2

Alternative Form

h_{1} \approx - 0.5 - 1.936492 i, h_{2} \approx - 0.5 + 1.936492 i, h_{3} = 2

Show Solution