Solve 15 s (1-s) (4 s^2)

Question

Simplify the expression

60 s^{3} - 60 s^{4}

Evaluate

15 s (1 - s) \times 4 s^{2}

Multiply the terms

60 s (1 - s) s^{2}

Multiply the terms with the same base by adding their exponents

60 s^{1 + 2} (1 - s)

Add the numbers

60 s^{3} (1 - s)

Apply the distributive property

60 s^{3} \times 1 - 60 s^{3} \times s

Any expression multiplied by 1 remains the same

60 s^{3} - 60 s^{3} \times s

Solution

More Steps

Evaluate

s^{3} \times s

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

s^{3 + 1}

Add the numbers

s^{4}

60 s^{3} - 60 s^{4}

Show Solution

s_{1} = 0, s_{2} = 1

Evaluate

15 s (1 - s) (4 s^{2})

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

15 s (1 - s) (4 s^{2}) = 0

Multiply the terms

15 s (1 - s) \times 4 s^{2} = 0

Multiply

More Steps

Multiply the terms

15 s (1 - s) \times 4 s^{2}

Multiply the terms

60 s (1 - s) s^{2}

Multiply the terms with the same base by adding their exponents

60 s^{1 + 2} (1 - s)

Add the numbers

60 s^{3} (1 - s)

60 s^{3} (1 - s) = 0

Elimination the left coefficient

s^{3} (1 - s) = 0

Separate the equation into 2 possible cases

s^{3} = 0 1 - s = 0

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

s = 0 1 - s = 0

Solve the equation

More Steps

Evaluate

1 - s = 0

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

- s = 0 - 1

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

- s = - 1

Change the signs on both sides of the equation

s = 1

s = 0 s = 1

Solution

s_{1} = 0, s_{2} = 1

Show Solution