Solve 5w(-7w^3)-2w(13-9w^(2))

Question

Simplify the expression

- 35 w^{4} - 26 w + 18 w^{3}

Evaluate

5 w (- 7 w^{3}) - 2 w (13 - 9 w^{2})

Multiply

More Steps

Multiply the terms

5 w (- 7 w^{3})

Rewrite the expression

- 5 w \times 7 w^{3}

Multiply the terms

- 35 w \times w^{3}

Multiply the terms with the same base by adding their exponents

- 35 w^{1 + 3}

Add the numbers

- 35 w^{4}

- 35 w^{4} - 2 w (13 - 9 w^{2})

Solution

More Steps

Evaluate

- 2 w (13 - 9 w^{2})

Apply the distributive property

- 2 w \times 13 - (- 2 w \times 9 w^{2})

Multiply the numbers

- 26 w - (- 2 w \times 9 w^{2})

Multiply the terms

More Steps

Evaluate

- 2 w \times 9 w^{2}

Multiply the numbers

- 18 w \times w^{2}

Multiply the terms

- 18 w^{3}

- 26 w - (- 18 w^{3})

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

- 26 w + 18 w^{3}

- 35 w^{4} - 26 w + 18 w^{3}

Show Solution

Factor the expression

- w (35 w^{3} + 26 - 18 w^{2})

Evaluate

5 w (- 7 w^{3}) - 2 w (13 - 9 w^{2})

Multiply

More Steps

Evaluate

5 w (- 7 w^{3})

Rewrite the expression

- 5 w \times 7 w^{3}

Multiply the terms

- 35 w \times w^{3}

Multiply the terms with the same base by adding their exponents

- 35 w^{1 + 3}

Add the numbers

- 35 w^{4}

- 35 w^{4} - 2 w (13 - 9 w^{2})

Rewrite the expression

- w \times 35 w^{3} - w \times 2 (13 - 9 w^{2})

Factor out - w from the expression

- w (35 w^{3} + 2 (13 - 9 w^{2}))

Solution

- w (35 w^{3} + 26 - 18 w^{2})

Show Solution

Find the roots

w_{1} \approx - 0.762708, w_{2} = 0

Evaluate

5 w (- 7 w^{3}) - 2 w (13 - 9 w^{2})

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

5 w (- 7 w^{3}) - 2 w (13 - 9 w^{2}) = 0

Multiply

More Steps

Multiply the terms

5 w (- 7 w^{3})

Rewrite the expression

- 5 w \times 7 w^{3}

Multiply the terms

- 35 w \times w^{3}

Multiply the terms with the same base by adding their exponents

- 35 w^{1 + 3}

Add the numbers

- 35 w^{4}

- 35 w^{4} - 2 w (13 - 9 w^{2}) = 0

Calculate

More Steps

Evaluate

- 2 w (13 - 9 w^{2})

Apply the distributive property

- 2 w \times 13 - (- 2 w \times 9 w^{2})

Multiply the numbers

- 26 w - (- 2 w \times 9 w^{2})

Multiply the terms

More Steps

Evaluate

- 2 w \times 9 w^{2}

Multiply the numbers

- 18 w \times w^{2}

Multiply the terms

- 18 w^{3}

- 26 w - (- 18 w^{3})

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

- 26 w + 18 w^{3}

- 35 w^{4} - 26 w + 18 w^{3} = 0

Factor the expression

- w (35 w^{3} + 26 - 18 w^{2}) = 0

Separate the equation into 2 possible cases

- w = 0 35 w^{3} + 26 - 18 w^{2} = 0

Change the signs on both sides of the equation

w = 0 35 w^{3} + 26 - 18 w^{2} = 0

Solve the equation

w = 0 w \approx - 0.762708

Solution

w_{1} \approx - 0.762708, w_{2} = 0

Show Solution