Solve 5f-3f-2f 9f^3f

Question

Simplify the expression

2 f - 18 f^{5}

Evaluate

5 f - 3 f - 2 f \times 9 f^{3} \times f

Multiply

More Steps

Multiply the terms

- 2 f \times 9 f^{3} \times f

Multiply the terms

- 18 f \times f^{3} \times f

Multiply the terms with the same base by adding their exponents

- 18 f^{1 + 3 + 1}

Add the numbers

- 18 f^{5}

5 f - 3 f - 18 f^{5}

Solution

More Steps

Evaluate

5 f - 3 f

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

(5 - 3) f

Subtract the numbers

2 f

2 f - 18 f^{5}

Show Solution

Factor the expression

2 f (1 - 3 f^{2}) (1 + 3 f^{2})

Evaluate

5 f - 3 f - 2 f \times 9 f^{3} \times f

Multiply

More Steps

Multiply the terms

2 f \times 9 f^{3} \times f

Multiply the terms

18 f \times f^{3} \times f

Multiply the terms with the same base by adding their exponents

18 f^{1 + 3 + 1}

Add the numbers

18 f^{5}

5 f - 3 f - 18 f^{5}

Subtract the terms

More Steps

Simplify

5 f - 3 f

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

(5 - 3) f

Subtract the numbers

2 f

2 f - 18 f^{5}

Rewrite the expression

2 f - 2 f \times 9 f^{4}

Factor out 2 f from the expression

2 f (1 - 9 f^{4})

Solution

2 f (1 - 3 f^{2}) (1 + 3 f^{2})

Show Solution

Find the roots

f_{1} = - \frac{3}{3}, f_{2} = 0, f_{3} = \frac{3}{3}

Alternative Form

f_{1} \approx - 0.57735, f_{2} = 0, f_{3} \approx 0.57735

Evaluate

5 f - 3 f - 2 f \times 9 f^{3} \times f

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

5 f - 3 f - 2 f \times 9 f^{3} \times f = 0

Multiply

More Steps

Multiply the terms

2 f \times 9 f^{3} \times f

Multiply the terms

18 f \times f^{3} \times f

Multiply the terms with the same base by adding their exponents

18 f^{1 + 3 + 1}

Add the numbers

18 f^{5}

5 f - 3 f - 18 f^{5} = 0

Subtract the terms

More Steps

Simplify

5 f - 3 f

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

(5 - 3) f

Subtract the numbers

2 f

2 f - 18 f^{5} = 0

Factor the expression

2 f (1 - 9 f^{4}) = 0

Divide both sides

f (1 - 9 f^{4}) = 0

Separate the equation into 2 possible cases

f = 0 1 - 9 f^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 9 f^{4} = 0

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

- 9 f^{4} = 0 - 1

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

- 9 f^{4} = - 1

Change the signs on both sides of the equation

9 f^{4} = 1

Divide both sides

\frac{9 f ^{4}}{9} = \frac{1}{9}

Divide the numbers

f^{4} = \frac{1}{9}

Take the root of both sides of the equation and remember to use both positive and negative roots

f = \pm 4 \frac{1}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{9}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 1}{4 9}

Simplify the radical expression

\frac{1}{4 9}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3}{3}

f = \pm \frac{3}{3}

Separate the equation into 2 possible cases

f = \frac{3}{3} f = - \frac{3}{3}

f = 0 f = \frac{3}{3} f = - \frac{3}{3}

Solution

f_{1} = - \frac{3}{3}, f_{2} = 0, f_{3} = \frac{3}{3}

Alternative Form

f_{1} \approx - 0.57735, f_{2} = 0, f_{3} \approx 0.57735

Show Solution