Solve ( - 5f^29f^5)-(f^29f^4)

Question

Simplify the expression

- 45 f^{7} - 9 f^{6}

Evaluate

(- 5 f^{2} \times 9 f^{5}) - (f^{2} \times 9 f^{4})

Multiply

More Steps

Multiply the terms

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

Multiply the terms

- 45 f^{2} \times f^{5}

Multiply the terms with the same base by adding their exponents

- 45 f^{2 + 5}

Add the numbers

- 45 f^{7}

(- 45 f^{7}) - (f^{2} \times 9 f^{4})

Remove the parentheses

- 45 f^{7} - (f^{2} \times 9 f^{4})

Solution

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

f^{2 + 4} \times 9

Add the numbers

f^{6} \times 9

Use the commutative property to reorder the terms

9 f^{6}

- 45 f^{7} - 9 f^{6}

Show Solution

Factor the expression

- 9 f^{6} (5 f + 1)

Evaluate

(- 5 f^{2} \times 9 f^{5}) - (f^{2} \times 9 f^{4})

Multiply

More Steps

Multiply the terms

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

Multiply the terms

- 45 f^{2} \times f^{5}

Multiply the terms with the same base by adding their exponents

- 45 f^{2 + 5}

Add the numbers

- 45 f^{7}

- 45 f^{7} - (f^{2} \times 9 f^{4})

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

f^{2 + 4} \times 9

Add the numbers

f^{6} \times 9

Use the commutative property to reorder the terms

9 f^{6}

- 45 f^{7} - 9 f^{6}

Rewrite the expression

- 9 f^{6} \times 5 f - 9 f^{6}

Solution

- 9 f^{6} (5 f + 1)

Show Solution

Find the roots

f_{1} = - \frac{1}{5}, f_{2} = 0

Alternative Form

f_{1} = - 0.2, f_{2} = 0

Evaluate

(- 5 f^{2} \times 9 f^{5}) - (f^{2} \times 9 f^{4})

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

(- 5 f^{2} \times 9 f^{5}) - (f^{2} \times 9 f^{4}) = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

- 45 f^{2} \times f^{5}

Multiply the terms with the same base by adding their exponents

- 45 f^{2 + 5}

Add the numbers

- 45 f^{7}

(- 45 f^{7}) - (f^{2} \times 9 f^{4}) = 0

Remove the parentheses

- 45 f^{7} - (f^{2} \times 9 f^{4}) = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

f^{2 + 4} \times 9

Add the numbers

f^{6} \times 9

Use the commutative property to reorder the terms

9 f^{6}

- 45 f^{7} - 9 f^{6} = 0

Factor the expression

- 9 f^{6} (5 f + 1) = 0

Divide both sides

f^{6} (5 f + 1) = 0

Separate the equation into 2 possible cases

f^{6} = 0 5 f + 1 = 0

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

f = 0 5 f + 1 = 0

Solve the equation

More Steps

Evaluate

5 f + 1 = 0

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

5 f = 0 - 1

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

5 f = - 1

Divide both sides

\frac{5 f}{5} = \frac{- 1}{5}

Divide the numbers

f = \frac{- 1}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

f = - \frac{1}{5}

f = 0 f = - \frac{1}{5}

Solution

f_{1} = - \frac{1}{5}, f_{2} = 0

Alternative Form

f_{1} = - 0.2, f_{2} = 0

Show Solution