Solve (3x^2-6x^4) (5x^2 2x 1)

Question

Simplify the expression

30 x^{5} - 60 x^{7}

Evaluate

(3 x^{2} - 6 x^{4}) (5 x^{2} \times 2 x \times 1)

Remove the parentheses

(3 x^{2} - 6 x^{4}) \times 5 x^{2} \times 2 x \times 1

Rewrite the expression

(3 x^{2} - 6 x^{4}) \times 5 x^{2} \times 2 x

Multiply the terms

(3 x^{2} - 6 x^{4}) \times 10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

(3 x^{2} - 6 x^{4}) \times 10 x^{2 + 1}

Add the numbers

(3 x^{2} - 6 x^{4}) \times 10 x^{3}

Multiply the terms

10 x^{3} (3 x^{2} - 6 x^{4})

Apply the distributive property

10 x^{3} \times 3 x^{2} - 10 x^{3} \times 6 x^{4}

Multiply the terms

More Steps

Evaluate

10 x^{3} \times 3 x^{2}

Multiply the numbers

30 x^{3} \times x^{2}

Multiply the terms

More Steps

Evaluate

x^{3} \times x^{2}

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

x^{3 + 2}

Add the numbers

x^{5}

30 x^{5}

30 x^{5} - 10 x^{3} \times 6 x^{4}

Solution

More Steps

Evaluate

10 x^{3} \times 6 x^{4}

Multiply the numbers

60 x^{3} \times x^{4}

Multiply the terms

More Steps

Evaluate

x^{3} \times x^{4}

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

x^{3 + 4}

Add the numbers

x^{7}

60 x^{7}

30 x^{5} - 60 x^{7}

Show Solution

Factor the expression

30 x^{5} (1 - 2 x^{2})

Evaluate

(3 x^{2} - 6 x^{4}) (5 x^{2} \times 2 x \times 1)

Remove the parentheses

(3 x^{2} - 6 x^{4}) \times 5 x^{2} \times 2 x \times 1

Multiply the terms

More Steps

Multiply the terms

5 x^{2} \times 2 x \times 1

Rewrite the expression

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

(3 x^{2} - 6 x^{4}) \times 10 x^{3}

Multiply the terms

10 x^{3} (3 x^{2} - 6 x^{4})

Factor the expression

More Steps

Evaluate

3 x^{2} - 6 x^{4}

Rewrite the expression

3 x^{2} - 3 x^{2} \times 2 x^{2}

Factor out 3 x^{2} from the expression

3 x^{2} (1 - 2 x^{2})

10 x^{3} \times 3 x^{2} (1 - 2 x^{2})

Solution

30 x^{5} (1 - 2 x^{2})

Show Solution

Find the roots

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

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Evaluate

(3 x^{2} - 6 x^{4}) (5 x^{2} \times 2 x \times 1)

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

(3 x^{2} - 6 x^{4}) (5 x^{2} \times 2 x \times 1) = 0

Multiply the terms

More Steps

Multiply the terms

5 x^{2} \times 2 x \times 1

Rewrite the expression

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

(3 x^{2} - 6 x^{4}) \times 10 x^{3} = 0

Multiply the terms

10 x^{3} (3 x^{2} - 6 x^{4}) = 0

Elimination the left coefficient

x^{3} (3 x^{2} - 6 x^{4}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 3 x^{2} - 6 x^{4} = 0

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

x = 0 3 x^{2} - 6 x^{4} = 0

Solve the equation

More Steps

Evaluate

3 x^{2} - 6 x^{4} = 0

Factor the expression

3 x^{2} (1 - 2 x^{2}) = 0

Divide both sides

x^{2} (1 - 2 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 2 x^{2} = 0

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

x = 0 1 - 2 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 2 x^{2} = 0

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

- 2 x^{2} = 0 - 1

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

- 2 x^{2} = - 1

Change the signs on both sides of the equation

2 x^{2} = 1

Divide both sides

\frac{2 x ^{2}}{2} = \frac{1}{2}

Divide the numbers

x^{2} = \frac{1}{2}

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

x = \pm \frac{1}{2}

Simplify the expression

x = \pm \frac{2}{2}

Separate the equation into 2 possible cases

x = \frac{2}{2} x = - \frac{2}{2}

x = 0 x = \frac{2}{2} x = - \frac{2}{2}

x = 0 x = 0 x = \frac{2}{2} x = - \frac{2}{2}

Find the union

x = 0 x = \frac{2}{2} x = - \frac{2}{2}

Solution

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

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Show Solution