Solve (-x^4)(5x^5)(3x-4)

Question

Simplify the expression

- 15 x^{10} + 20 x^{9}

Evaluate

(- x^{4}) \times 5 x^{5} (3 x - 4)

Remove the parentheses

- x^{4} \times 5 x^{5} (3 x - 4)

Multiply the terms with the same base by adding their exponents

- x^{4 + 5} \times 5 (3 x - 4)

Add the numbers

- x^{9} \times 5 (3 x - 4)

Use the commutative property to reorder the terms

- 5 x^{9} (3 x - 4)

Apply the distributive property

- 5 x^{9} \times 3 x - (- 5 x^{9} \times 4)

Multiply the terms

More Steps

Evaluate

- 5 x^{9} \times 3 x

Multiply the numbers

- 15 x^{9} \times x

Multiply the terms

More Steps

Evaluate

x^{9} \times x

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

x^{9 + 1}

Add the numbers

x^{10}

- 15 x^{10}

- 15 x^{10} - (- 5 x^{9} \times 4)

Multiply the numbers

- 15 x^{10} - (- 20 x^{9})

Solution

- 15 x^{10} + 20 x^{9}

Show Solution

x_{1} = 0, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}

Evaluate

(- x^{4}) (5 x^{5}) (3 x - 4)

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

(- x^{4}) (5 x^{5}) (3 x - 4) = 0

Remove the parentheses

- x^{4} (5 x^{5}) (3 x - 4) = 0

Multiply the terms

- x^{4} \times 5 x^{5} (3 x - 4) = 0

Multiply

More Steps

Multiply the terms

- x^{4} \times 5 x^{5} (3 x - 4)

Multiply the terms with the same base by adding their exponents

- x^{4 + 5} \times 5 (3 x - 4)

Add the numbers

- x^{9} \times 5 (3 x - 4)

Use the commutative property to reorder the terms

- 5 x^{9} (3 x - 4)

- 5 x^{9} (3 x - 4) = 0

Change the sign

5 x^{9} (3 x - 4) = 0

Elimination the left coefficient

x^{9} (3 x - 4) = 0

Separate the equation into 2 possible cases

x^{9} = 0 3 x - 4 = 0

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

x = 0 3 x - 4 = 0

Solve the equation

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = 0 x = \frac{4}{3}

Solution

x_{1} = 0, x_{2} = \frac{4}{3}

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}

Show Solution