Solve (4v^28v 7)-(2v^5)

Question

Simplify the expression

224 v^{3} - 2 v^{5}

Evaluate

(4 v^{2} \times 8 v \times 7) - 2 v^{5}

Solution

More Steps

Evaluate

4 v^{2} \times 8 v \times 7

Multiply the terms

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Evaluate

4 \times 8 \times 7

Multiply the terms

32 \times 7

Multiply the numbers

224

224 v^{2} \times v

Multiply the terms with the same base by adding their exponents

224 v^{2 + 1}

Add the numbers

224 v^{3}

224 v^{3} - 2 v^{5}

Show Solution

Factor the expression

2 v^{3} (112 - v^{2})

Evaluate

(4 v^{2} \times 8 v \times 7) - 2 v^{5}

Multiply

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Evaluate

4 v^{2} \times 8 v \times 7

Multiply the terms

More Steps

Evaluate

4 \times 8 \times 7

Multiply the terms

32 \times 7

Multiply the numbers

224

224 v^{2} \times v

Multiply the terms with the same base by adding their exponents

224 v^{2 + 1}

Add the numbers

224 v^{3}

224 v^{3} - 2 v^{5}

Rewrite the expression

2 v^{3} \times 112 - 2 v^{3} \times v^{2}

Solution

2 v^{3} (112 - v^{2})

Show Solution

Find the roots

v_{1} = - 47, v_{2} = 0, v_{3} = 47

Alternative Form

v_{1} \approx - 10.583005, v_{2} = 0, v_{3} \approx 10.583005

Evaluate

(4 v^{2} \times 8 v \times 7) - (2 v^{5})

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

(4 v^{2} \times 8 v \times 7) - (2 v^{5}) = 0

Multiply

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Multiply the terms

4 v^{2} \times 8 v \times 7

Multiply the terms

More Steps

Evaluate

4 \times 8 \times 7

Multiply the terms

32 \times 7

Multiply the numbers

224

224 v^{2} \times v

Multiply the terms with the same base by adding their exponents

224 v^{2 + 1}

Add the numbers

224 v^{3}

224 v^{3} - (2 v^{5}) = 0

Multiply the terms

224 v^{3} - 2 v^{5} = 0

Factor the expression

2 v^{3} (112 - v^{2}) = 0

Divide both sides

v^{3} (112 - v^{2}) = 0

Separate the equation into 2 possible cases

v^{3} = 0 112 - v^{2} = 0

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

v = 0 112 - v^{2} = 0

Solve the equation

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Evaluate

112 - v^{2} = 0

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

- v^{2} = 0 - 112

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

- v^{2} = - 112

Change the signs on both sides of the equation

v^{2} = 112

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

v = \pm 112

Simplify the expression

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Evaluate

112

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

16 \times 7

Write the number in exponential form with the base of 4

4^{2} \times 7

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

4^{2} \times 7

Reduce the index of the radical and exponent with 2

47

v = \pm 47

Separate the equation into 2 possible cases

v = 47 v = - 47

v = 0 v = 47 v = - 47

Solution

v_{1} = - 47, v_{2} = 0, v_{3} = 47

Alternative Form

v_{1} \approx - 10.583005, v_{2} = 0, v_{3} \approx 10.583005

Show Solution