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

Question

Simplify the expression

6 x^{10} - 10 x^{7}

Evaluate

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

Remove the parentheses

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

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

Multiply the numbers

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

Multiply the terms

More Steps

Evaluate

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

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

x^{6 + 4}

Add the numbers

x^{10}

6 x^{10}

6 x^{10} - 2 x^{6} \times 5 x

Solution

More Steps

Evaluate

2 x^{6} \times 5 x

Multiply the numbers

10 x^{6} \times x

Multiply the terms

More Steps

Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

10 x^{7}

6 x^{10} - 10 x^{7}

Show Solution

Factor the expression

2 x^{7} (3 x^{3} - 5)

Evaluate

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

Remove the parentheses

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

Multiply the terms

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x^{4}

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 2

Add the numbers

x^{6} \times 2

Use the commutative property to reorder the terms

2 x^{6}

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

Multiply the terms

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

Factor the expression

More Steps

Evaluate

3 x^{4} - 5 x

Rewrite the expression

x \times 3 x^{3} - x \times 5

Factor out x from the expression

x (3 x^{3} - 5)

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

Solution

2 x^{7} (3 x^{3} - 5)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 45}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 1.185631

Evaluate

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

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

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

Multiply the terms

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x^{4}

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 2

Add the numbers

x^{6} \times 2

Use the commutative property to reorder the terms

2 x^{6}

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

Multiply the terms

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

Elimination the left coefficient

x^{6} (3 x^{4} - 5 x) = 0

Separate the equation into 2 possible cases

x^{6} = 0 3 x^{4} - 5 x = 0

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

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

Solve the equation

More Steps

Evaluate

3 x^{4} - 5 x = 0

Factor the expression

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

Separate the equation into 2 possible cases

x = 0 3 x^{3} - 5 = 0

Solve the equation

More Steps

Evaluate

3 x^{3} - 5 = 0

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

3 x^{3} = 0 + 5

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

3 x^{3} = 5

Divide both sides

\frac{3 x ^{3}}{3} = \frac{5}{3}

Divide the numbers

x^{3} = \frac{5}{3}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{5}{3}

Calculate

x = 3 \frac{5}{3}

Simplify the root

x = \frac{3 45}{3}

x = 0 x = \frac{3 45}{3}

x = 0 x = 0 x = \frac{3 45}{3}

Find the union

x = 0 x = \frac{3 45}{3}

Solution

x_{1} = 0, x_{2} = \frac{3 45}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 1.185631

Show Solution