Solve ( - 8y^37y^22y 9)-( - 4y 1)

Question

Simplify the expression

- 1008 y^{6} + 4 y

Evaluate

(- 8 y^{3} \times 7 y^{2} \times 2 y \times 9) - (- 4 y \times 1)

Multiply

More Steps

Multiply the terms

- 8 y^{3} \times 7 y^{2} \times 2 y \times 9

Multiply the terms

More Steps

Evaluate

8 \times 7 \times 2 \times 9

Multiply the terms

56 \times 2 \times 9

Multiply the terms

112 \times 9

Multiply the numbers

1008

- 1008 y^{3} \times y^{2} \times y

Multiply the terms with the same base by adding their exponents

- 1008 y^{3 + 2 + 1}

Add the numbers

- 1008 y^{6}

(- 1008 y^{6}) - (- 4 y \times 1)

Remove the parentheses

- 1008 y^{6} - (- 4 y \times 1)

Multiply the terms

- 1008 y^{6} - (- 4 y)

Solution

- 1008 y^{6} + 4 y

Show Solution

Factor the expression

- 4 y (252 y^{5} - 1)

Evaluate

(- 8 y^{3} \times 7 y^{2} \times 2 y \times 9) - (- 4 y \times 1)

Multiply

More Steps

Multiply the terms

- 8 y^{3} \times 7 y^{2} \times 2 y \times 9

Multiply the terms

More Steps

Evaluate

8 \times 7 \times 2 \times 9

Multiply the terms

56 \times 2 \times 9

Multiply the terms

112 \times 9

Multiply the numbers

1008

- 1008 y^{3} \times y^{2} \times y

Multiply the terms with the same base by adding their exponents

- 1008 y^{3 + 2 + 1}

Add the numbers

- 1008 y^{6}

- 1008 y^{6} - (- 4 y \times 1)

Multiply the terms

- 1008 y^{6} - (- 4 y)

Rewrite the expression

- 1008 y^{6} + 4 y

Rewrite the expression

- 4 y \times 252 y^{5} + 4 y

Solution

- 4 y (252 y^{5} - 1)

Show Solution

Find the roots

y_{1} = 0, y_{2} = \frac{5 25 2 ^{4}}{252}

Alternative Form

y_{1} = 0, y_{2} \approx 0.330918

Evaluate

(- 8 y^{3} \times 7 y^{2} \times 2 y \times 9) - (- 4 y \times 1)

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

(- 8 y^{3} \times 7 y^{2} \times 2 y \times 9) - (- 4 y \times 1) = 0

Multiply

More Steps

Multiply the terms

- 8 y^{3} \times 7 y^{2} \times 2 y \times 9

Multiply the terms

More Steps

Evaluate

8 \times 7 \times 2 \times 9

Multiply the terms

56 \times 2 \times 9

Multiply the terms

112 \times 9

Multiply the numbers

1008

- 1008 y^{3} \times y^{2} \times y

Multiply the terms with the same base by adding their exponents

- 1008 y^{3 + 2 + 1}

Add the numbers

- 1008 y^{6}

(- 1008 y^{6}) - (- 4 y \times 1) = 0

Remove the parentheses

- 1008 y^{6} - (- 4 y \times 1) = 0

Multiply the terms

- 1008 y^{6} - (- 4 y) = 0

Rewrite the expression

- 1008 y^{6} + 4 y = 0

Factor the expression

4 y (- 252 y^{5} + 1) = 0

Divide both sides

y (- 252 y^{5} + 1) = 0

Separate the equation into 2 possible cases

y = 0 - 252 y^{5} + 1 = 0

Solve the equation

More Steps

Evaluate

- 252 y^{5} + 1 = 0

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

- 252 y^{5} = 0 - 1

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

- 252 y^{5} = - 1

Change the signs on both sides of the equation

252 y^{5} = 1

Divide both sides

\frac{252 y ^{5}}{252} = \frac{1}{252}

Divide the numbers

y^{5} = \frac{1}{252}

Take the 5 -th root on both sides of the equation

5 y^{5} = 5 \frac{1}{252}

Calculate

y = 5 \frac{1}{252}

Simplify the root

More Steps

Evaluate

5 \frac{1}{252}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5 1}{5 252}

Simplify the radical expression

\frac{1}{5 252}

Multiply by the Conjugate

\frac{5 25 2 ^{4}}{5 252 \times 5 25 2 ^{4}}

Multiply the numbers

\frac{5 25 2 ^{4}}{252}

y = \frac{5 25 2 ^{4}}{252}

y = 0 y = \frac{5 25 2 ^{4}}{252}

Solution

y_{1} = 0, y_{2} = \frac{5 25 2 ^{4}}{252}

Alternative Form

y_{1} = 0, y_{2} \approx 0.330918

Show Solution