Solve -2y^3-2y^22y^2

Question

Simplify the expression

- 2 y^{3} - 4 y^{4}

Evaluate

- 2 y^{3} - 2 y^{2} \times 2 y^{2}

Solution

More Steps

Evaluate

2 y^{2} \times 2 y^{2}

Multiply the terms

4 y^{2} \times y^{2}

Multiply the terms with the same base by adding their exponents

4 y^{2 + 2}

Add the numbers

4 y^{4}

- 2 y^{3} - 4 y^{4}

Show Solution

- 2 y^{3} (1 + 2 y)

Evaluate

- 2 y^{3} - 2 y^{2} \times 2 y^{2}

Multiply

More Steps

Evaluate

2 y^{2} \times 2 y^{2}

Multiply the terms

4 y^{2} \times y^{2}

Multiply the terms with the same base by adding their exponents

4 y^{2 + 2}

Add the numbers

4 y^{4}

- 2 y^{3} - 4 y^{4}

Rewrite the expression

- 2 y^{3} - 2 y^{3} \times 2 y

Solution

- 2 y^{3} (1 + 2 y)

Show Solution

y_{1} = - \frac{1}{2}, y_{2} = 0

Alternative Form

y_{1} = - 0.5, y_{2} = 0

Evaluate

- 2 y^{3} - 2 y^{2} \times 2 y^{2}

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

- 2 y^{3} - 2 y^{2} \times 2 y^{2} = 0

Multiply

More Steps

Multiply the terms

2 y^{2} \times 2 y^{2}

Multiply the terms

4 y^{2} \times y^{2}

Multiply the terms with the same base by adding their exponents

4 y^{2 + 2}

Add the numbers

4 y^{4}

- 2 y^{3} - 4 y^{4} = 0

Factor the expression

- 2 y^{3} (1 + 2 y) = 0

Divide both sides

y^{3} (1 + 2 y) = 0

Separate the equation into 2 possible cases

y^{3} = 0 1 + 2 y = 0

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

y = 0 1 + 2 y = 0

Solve the equation

More Steps

Evaluate

1 + 2 y = 0

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

2 y = 0 - 1

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

2 y = - 1

Divide both sides

\frac{2 y}{2} = \frac{- 1}{2}

Divide the numbers

y = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y = - \frac{1}{2}

y = 0 y = - \frac{1}{2}

Solution

y_{1} = - \frac{1}{2}, y_{2} = 0

Alternative Form

y_{1} = - 0.5, y_{2} = 0

Show Solution