Solve 4r(-2r^2+2r+2)

Question

Simplify the expression

Solution

- 8 r^{3} + 8 r^{2} + 8 r

Evaluate

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

Apply the distributive property

4 r (- 2 r^{2}) + 4 r \times 2 r + 4 r \times 2

Multiply the terms

More Steps

Evaluate

4 r (- 2 r^{2})

Multiply the numbers

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Evaluate

4 (- 2)

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

- 4 \times 2

Multiply the numbers

- 8

- 8 r \times r^{2}

Multiply the terms

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Evaluate

r \times r^{2}

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

r^{1 + 2}

Add the numbers

r^{3}

- 8 r^{3}

- 8 r^{3} + 4 r \times 2 r + 4 r \times 2

Multiply the terms

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Evaluate

4 r \times 2 r

Multiply the numbers

8 r \times r

Multiply the terms

8 r^{2}

- 8 r^{3} + 8 r^{2} + 4 r \times 2

Solution

- 8 r^{3} + 8 r^{2} + 8 r

Show Solution

Factor the expression

Factor

- 8 r (r^{2} - r - 1)

Evaluate

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

Factor the expression

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

Solution

- 8 r (r^{2} - r - 1)

Show Solution

Find the roots

Find the roots of the algebra expression

r_{1} = \frac{1 - 5}{2}, r_{2} = 0, r_{3} = \frac{1 + 5}{2}

Alternative Form

r_{1} \approx - 0.618034, r_{2} = 0, r_{3} \approx 1.618034

Evaluate

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

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

4 r (- 2 r^{2} + 2 r + 2) = 0

Elimination the left coefficient

r (- 2 r^{2} + 2 r + 2) = 0

Separate the equation into 2 possible cases

r = 0 - 2 r^{2} + 2 r + 2 = 0

Solve the equation

More Steps

Evaluate

- 2 r^{2} + 2 r + 2 = 0

Multiply both sides

2 r^{2} - 2 r - 2 = 0

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

r = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 ( - 2 )}{2 \times 2}

Simplify the expression

r = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 ( - 2 )}{4}

Simplify the expression

More Steps

Evaluate

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

Multiply

(- 2)^{2} - (- 16)

Rewrite the expression

2^{2} - (- 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^{2} + 16

Evaluate the power

4 + 16

Add the numbers

20

r = \frac{2 \pm 20}{4}

Simplify the radical expression

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Evaluate

20

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

The root of a product is equal to the product of the roots of each factor

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

r = \frac{2 \pm 2 5}{4}

Separate the equation into 2 possible cases

r = \frac{2 + 2 5}{4} r = \frac{2 - 2 5}{4}

Simplify the expression

r = \frac{1 + 5}{2} r = \frac{2 - 2 5}{4}

Simplify the expression

r = \frac{1 + 5}{2} r = \frac{1 - 5}{2}

r = 0 r = \frac{1 + 5}{2} r = \frac{1 - 5}{2}

Solution

r_{1} = \frac{1 - 5}{2}, r_{2} = 0, r_{3} = \frac{1 + 5}{2}

Alternative Form

r_{1} \approx - 0.618034, r_{2} = 0, r_{3} \approx 1.618034

Show Solution

4r( 2r^2+2r+2)

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression