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

Question

Simplify the expression

- 4 y^{4} - 20 y^{3}

Evaluate

(- y - 5) (9 y^{3} - 5 y^{3})

Subtract the terms

More Steps

Simplify

9 y^{3} - 5 y^{3}

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

(9 - 5) y^{3}

Subtract the numbers

4 y^{3}

(- y - 5) \times 4 y^{3}

Multiply the terms

4 y^{3} (- y - 5)

Apply the distributive property

4 y^{3} (- y) - 4 y^{3} \times 5

Multiply the terms

More Steps

Evaluate

4 y^{3} (- y)

Multiply the numbers

- 4 y^{3} \times y

Multiply the terms

More Steps

Evaluate

y^{3} \times y

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

y^{3 + 1}

Add the numbers

y^{4}

- 4 y^{4}

- 4 y^{4} - 4 y^{3} \times 5

Solution

- 4 y^{4} - 20 y^{3}

Show Solution

y_{1} = - 5, y_{2} = 0

Evaluate

(- y - 5) (9 y^{3} - 5 y^{3})

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

(- y - 5) (9 y^{3} - 5 y^{3}) = 0

Subtract the terms

More Steps

Simplify

9 y^{3} - 5 y^{3}

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

(9 - 5) y^{3}

Subtract the numbers

4 y^{3}

(- y - 5) \times 4 y^{3} = 0

Multiply the terms

4 y^{3} (- y - 5) = 0

Elimination the left coefficient

y^{3} (- y - 5) = 0

Separate the equation into 2 possible cases

y^{3} = 0 - y - 5 = 0

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

y = 0 - y - 5 = 0

Solve the equation

More Steps

Evaluate

- y - 5 = 0

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

- y = 0 + 5

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

- y = 5

Change the signs on both sides of the equation

y = - 5

y = 0 y = - 5

Solution

y_{1} = - 5, y_{2} = 0

Show Solution