Solve 50w^4-25w^3-10w^25w

Question

Simplify the expression

50 w^{4} - 75 w^{3}

Evaluate

50 w^{4} - 25 w^{3} - 10 w^{2} \times 5 w

Multiply

More Steps

Multiply the terms

- 10 w^{2} \times 5 w

Multiply the terms

- 50 w^{2} \times w

Multiply the terms with the same base by adding their exponents

- 50 w^{2 + 1}

Add the numbers

- 50 w^{3}

50 w^{4} - 25 w^{3} - 50 w^{3}

Solution

More Steps

Evaluate

- 25 w^{3} - 50 w^{3}

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

(- 25 - 50) w^{3}

Subtract the numbers

- 75 w^{3}

50 w^{4} - 75 w^{3}

Show Solution

Factor the expression

25 w^{3} (2 w - 3)

Evaluate

50 w^{4} - 25 w^{3} - 10 w^{2} \times 5 w

Multiply

More Steps

Multiply the terms

10 w^{2} \times 5 w

Multiply the terms

50 w^{2} \times w

Multiply the terms with the same base by adding their exponents

50 w^{2 + 1}

Add the numbers

50 w^{3}

50 w^{4} - 25 w^{3} - 50 w^{3}

Subtract the terms

More Steps

Evaluate

- 25 w^{3} - 50 w^{3}

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

(- 25 - 50) w^{3}

Subtract the numbers

- 75 w^{3}

50 w^{4} - 75 w^{3}

Rewrite the expression

25 w^{3} \times 2 w - 25 w^{3} \times 3

Solution

25 w^{3} (2 w - 3)

Show Solution

Find the roots

w_{1} = 0, w_{2} = \frac{3}{2}

Alternative Form

w_{1} = 0, w_{2} = 1.5

Evaluate

50 w^{4} - 25 w^{3} - 10 w^{2} \times 5 w

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

50 w^{4} - 25 w^{3} - 10 w^{2} \times 5 w = 0

Multiply

More Steps

Multiply the terms

10 w^{2} \times 5 w

Multiply the terms

50 w^{2} \times w

Multiply the terms with the same base by adding their exponents

50 w^{2 + 1}

Add the numbers

50 w^{3}

50 w^{4} - 25 w^{3} - 50 w^{3} = 0

Subtract the terms

More Steps

Simplify

50 w^{4} - 25 w^{3} - 50 w^{3}

Subtract the terms

More Steps

Evaluate

- 25 w^{3} - 50 w^{3}

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

(- 25 - 50) w^{3}

Subtract the numbers

- 75 w^{3}

50 w^{4} - 75 w^{3}

50 w^{4} - 75 w^{3} = 0

Factor the expression

25 w^{3} (2 w - 3) = 0

Divide both sides

w^{3} (2 w - 3) = 0

Separate the equation into 2 possible cases

w^{3} = 0 2 w - 3 = 0

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

w = 0 2 w - 3 = 0

Solve the equation

More Steps

Evaluate

2 w - 3 = 0

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

2 w = 0 + 3

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

2 w = 3

Divide both sides

\frac{2 w}{2} = \frac{3}{2}

Divide the numbers

w = \frac{3}{2}

w = 0 w = \frac{3}{2}

Solution

w_{1} = 0, w_{2} = \frac{3}{2}

Alternative Form

w_{1} = 0, w_{2} = 1.5

Show Solution