Solve (-8y^2-9y) -(-8y^3 9y^2-5y)

Question

Simplify the expression

- 8 y^{2} - 4 y + 72 y^{5}

Evaluate

(- 8 y^{2} - 9 y) - (- 8 y^{3} \times 9 y^{2} - 5 y)

Remove the parentheses

- 8 y^{2} - 9 y - (- 8 y^{3} \times 9 y^{2} - 5 y)

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 72 y^{3 + 2}

Add the numbers

- 72 y^{5}

- 8 y^{2} - 9 y - (- 72 y^{5} - 5 y)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 y^{2} - 9 y + 72 y^{5} + 5 y

Solution

More Steps

Evaluate

- 9 y + 5 y

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

(- 9 + 5) y

Add the numbers

- 4 y

- 8 y^{2} - 4 y + 72 y^{5}

Show Solution

Factor the expression

- 4 y (2 y + 1 - 18 y^{4})

Evaluate

(- 8 y^{2} - 9 y) - (- 8 y^{3} \times 9 y^{2} - 5 y)

Remove the parentheses

- 8 y^{2} - 9 y - (- 8 y^{3} \times 9 y^{2} - 5 y)

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 72 y^{3 + 2}

Add the numbers

- 72 y^{5}

- 8 y^{2} - 9 y - (- 72 y^{5} - 5 y)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 y^{2} - 9 y + 72 y^{5} + 5 y

Add the terms

More Steps

Evaluate

- 9 y + 5 y

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

(- 9 + 5) y

Add the numbers

- 4 y

- 8 y^{2} - 4 y + 72 y^{5}

Rewrite the expression

- 4 y \times 2 y - 4 y + 4 y \times 18 y^{4}

Solution

- 4 y (2 y + 1 - 18 y^{4})

Show Solution

Find the roots

y_{1} \approx - 0.355787, y_{2} = 0, y_{3} \approx 0.589912

Evaluate

(- 8 y^{2} - 9 y) - (- 8 y^{3} \times 9 y^{2} - 5 y)

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

(- 8 y^{2} - 9 y) - (- 8 y^{3} \times 9 y^{2} - 5 y) = 0

Remove the parentheses

- 8 y^{2} - 9 y - (- 8 y^{3} \times 9 y^{2} - 5 y) = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 72 y^{3 + 2}

Add the numbers

- 72 y^{5}

- 8 y^{2} - 9 y - (- 72 y^{5} - 5 y) = 0

Subtract the terms

More Steps

Simplify

- 8 y^{2} - 9 y - (- 72 y^{5} - 5 y)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 y^{2} - 9 y + 72 y^{5} + 5 y

Add the terms

More Steps

Evaluate

- 9 y + 5 y

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

(- 9 + 5) y

Add the numbers

- 4 y

- 8 y^{2} - 4 y + 72 y^{5}

- 8 y^{2} - 4 y + 72 y^{5} = 0

Factor the expression

4 (- y) (2 y + 1 - 18 y^{4}) = 0

Divide both sides

- y (2 y + 1 - 18 y^{4}) = 0

Separate the equation into 2 possible cases

- y = 0 2 y + 1 - 18 y^{4} = 0

Change the signs on both sides of the equation

y = 0 2 y + 1 - 18 y^{4} = 0

Solve the equation

y = 0 y \approx - 0.355787 y \approx 0.589912

Solution

y_{1} \approx - 0.355787, y_{2} = 0, y_{3} \approx 0.589912

Show Solution