Solve 16v^4-8v^3-56v^228v

Question

Simplify the expression

16 v^{4} - 1576 v^{3}

Evaluate

16 v^{4} - 8 v^{3} - 56 v^{2} \times 28 v

Multiply

More Steps

Multiply the terms

- 56 v^{2} \times 28 v

Multiply the terms

- 1568 v^{2} \times v

Multiply the terms with the same base by adding their exponents

- 1568 v^{2 + 1}

Add the numbers

- 1568 v^{3}

16 v^{4} - 8 v^{3} - 1568 v^{3}

Solution

More Steps

Evaluate

- 8 v^{3} - 1568 v^{3}

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

(- 8 - 1568) v^{3}

Subtract the numbers

- 1576 v^{3}

16 v^{4} - 1576 v^{3}

Show Solution

Factor the expression

8 v^{3} (2 v - 197)

Evaluate

16 v^{4} - 8 v^{3} - 56 v^{2} \times 28 v

Multiply

More Steps

Multiply the terms

56 v^{2} \times 28 v

Multiply the terms

1568 v^{2} \times v

Multiply the terms with the same base by adding their exponents

1568 v^{2 + 1}

Add the numbers

1568 v^{3}

16 v^{4} - 8 v^{3} - 1568 v^{3}

Subtract the terms

More Steps

Evaluate

- 8 v^{3} - 1568 v^{3}

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

(- 8 - 1568) v^{3}

Subtract the numbers

- 1576 v^{3}

16 v^{4} - 1576 v^{3}

Rewrite the expression

8 v^{3} \times 2 v - 8 v^{3} \times 197

Solution

8 v^{3} (2 v - 197)

Show Solution

Find the roots

v_{1} = 0, v_{2} = \frac{197}{2}

Alternative Form

v_{1} = 0, v_{2} = 98.5

Evaluate

16 v^{4} - 8 v^{3} - 56 v^{2} \times 28 v

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

16 v^{4} - 8 v^{3} - 56 v^{2} \times 28 v = 0

Multiply

More Steps

Multiply the terms

56 v^{2} \times 28 v

Multiply the terms

1568 v^{2} \times v

Multiply the terms with the same base by adding their exponents

1568 v^{2 + 1}

Add the numbers

1568 v^{3}

16 v^{4} - 8 v^{3} - 1568 v^{3} = 0

Subtract the terms

More Steps

Simplify

16 v^{4} - 8 v^{3} - 1568 v^{3}

Subtract the terms

More Steps

Evaluate

- 8 v^{3} - 1568 v^{3}

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

(- 8 - 1568) v^{3}

Subtract the numbers

- 1576 v^{3}

16 v^{4} - 1576 v^{3}

16 v^{4} - 1576 v^{3} = 0

Factor the expression

8 v^{3} (2 v - 197) = 0

Divide both sides

v^{3} (2 v - 197) = 0

Separate the equation into 2 possible cases

v^{3} = 0 2 v - 197 = 0

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

v = 0 2 v - 197 = 0

Solve the equation

More Steps

Evaluate

2 v - 197 = 0

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

2 v = 0 + 197

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

2 v = 197

Divide both sides

\frac{2 v}{2} = \frac{197}{2}

Divide the numbers

v = \frac{197}{2}

v = 0 v = \frac{197}{2}

Solution

v_{1} = 0, v_{2} = \frac{197}{2}

Alternative Form

v_{1} = 0, v_{2} = 98.5

Show Solution