Solve (x-1/12x^3 24x^2) (3x^2/12x^3 24x^2)

Question

Simplify the expression

6 x^{8} - 12 x^{12}

Evaluate

(x - \frac{1}{12} x^{3} \times 24 x^{2}) ((3 \times \frac{x ^{2}}{12}) x^{3} \times 24 x^{2})

Remove the parentheses

(x - \frac{1}{12} x^{3} \times 24 x^{2}) \times 3 \times \frac{x ^{2}}{12} x^{3} \times 24 x^{2}

Multiply

More Steps

Multiply the terms

\frac{1}{12} x^{3} \times 24 x^{2}

Multiply the terms

More Steps

Evaluate

\frac{1}{12} \times 24

Reduce the numbers

1 \times 2

Simplify

2

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 2}

Add the numbers

2 x^{5}

(x - 2 x^{5}) \times 3 \times \frac{x ^{2}}{12} x^{3} \times 24 x^{2}

Multiply the terms

(x - 2 x^{5}) \times 72 \times \frac{x ^{2}}{12} x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

(x - 2 x^{5}) \times 72 \times \frac{x ^{2}}{12} x^{3 + 2}

Add the numbers

(x - 2 x^{5}) \times 72 \times \frac{x ^{2}}{12} x^{5}

Multiply the terms

More Steps

Evaluate

72 \times \frac{x ^{2}}{12} x^{5}

Cancel out the common factor 12

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

Multiply the terms

More Steps

Evaluate

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

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

x^{2 + 5}

Add the numbers

x^{7}

6 x^{7}

(x - 2 x^{5}) \times 6 x^{7}

Multiply the terms

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

Apply the distributive property

6 x^{7} \times x - 6 x^{7} \times 2 x^{5}

Multiply the terms

More Steps

Evaluate

x^{7} \times x

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

x^{7 + 1}

Add the numbers

x^{8}

6 x^{8} - 6 x^{7} \times 2 x^{5}

Solution

More Steps

Evaluate

6 x^{7} \times 2 x^{5}

Multiply the numbers

12 x^{7} \times x^{5}

Multiply the terms

More Steps

Evaluate

x^{7} \times x^{5}

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

x^{7 + 5}

Add the numbers

x^{12}

12 x^{12}

6 x^{8} - 12 x^{12}

Show Solution

Factor the expression

6 x^{8} (1 - 2 x^{4})

Evaluate

(x - \frac{1}{12} x^{3} \times 24 x^{2}) ((3 \times \frac{x ^{2}}{12}) x^{3} \times 24 x^{2})

Remove the parentheses

(x - \frac{1}{12} x^{3} \times 24 x^{2}) \times 3 \times \frac{x ^{2}}{12} x^{3} \times 24 x^{2}

Multiply

More Steps

Multiply the terms

\frac{1}{12} x^{3} \times 24 x^{2}

Multiply the terms

More Steps

Evaluate

\frac{1}{12} \times 24

Reduce the numbers

1 \times 2

Simplify

2

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 2}

Add the numbers

2 x^{5}

(x - 2 x^{5}) \times 3 \times \frac{x ^{2}}{12} x^{3} \times 24 x^{2}

Multiply the terms

More Steps

Multiply the terms

3 \times \frac{x ^{2}}{12}

Cancel out the common factor 3

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

Multiply the terms

\frac{x ^{2}}{4}

(x - 2 x^{5}) \times \frac{x ^{2}}{4} x^{3} \times 24 x^{2}

Multiply

More Steps

Multiply the terms

\frac{x ^{2}}{4} x^{3} \times 24 x^{2}

Multiply the terms with the same base by adding their exponents

\frac{x ^{2}}{4} x^{3 + 2} \times 24

Add the numbers

\frac{x ^{2}}{4} x^{5} \times 24

Multiply the terms

More Steps

Multiply the terms

\frac{x ^{2}}{4} x^{5}

Multiply the terms

\frac{x ^{2} \times x ^{5}}{4}

Multiply the terms

\frac{x ^{7}}{4}

\frac{x ^{7}}{4} \times 24

Cancel out the common factor 4

x^{7} \times 6

Use the commutative property to reorder the terms

6 x^{7}

(x - 2 x^{5}) \times 6 x^{7}

Multiply the terms

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

Factor the expression

More Steps

Evaluate

x - 2 x^{5}

Rewrite the expression

x - x \times 2 x^{4}

Factor out x from the expression

x (1 - 2 x^{4})

6 x^{7} \times x (1 - 2 x^{4})

Solution

6 x^{8} (1 - 2 x^{4})

Show Solution

Find the roots

x_{1} = - \frac{4 8}{2}, x_{2} = 0, x_{3} = \frac{4 8}{2}

Alternative Form

x_{1} \approx - 0.840896, x_{2} = 0, x_{3} \approx 0.840896

Evaluate

(x - \frac{1}{12} x^{3} \times 24 x^{2}) ((3 \times \frac{x ^{2}}{12}) x^{3} \times 24 x^{2})

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

(x - \frac{1}{12} x^{3} \times 24 x^{2}) ((3 \times \frac{x ^{2}}{12}) x^{3} \times 24 x^{2}) = 0

Multiply

More Steps

Multiply the terms

\frac{1}{12} x^{3} \times 24 x^{2}

Multiply the terms

More Steps

Evaluate

\frac{1}{12} \times 24

Reduce the numbers

1 \times 2

Simplify

2

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

Multiply the terms with the same base by adding their exponents

2 x^{3 + 2}

Add the numbers

2 x^{5}

(x - 2 x^{5}) ((3 \times \frac{x ^{2}}{12}) x^{3} \times 24 x^{2}) = 0

Multiply the terms

More Steps

Multiply the terms

3 \times \frac{x ^{2}}{12}

Cancel out the common factor 3

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

Multiply the terms

\frac{x ^{2}}{4}

(x - 2 x^{5}) (\frac{x ^{2}}{4} x^{3} \times 24 x^{2}) = 0

Multiply

More Steps

Multiply the terms

\frac{x ^{2}}{4} x^{3} \times 24 x^{2}

Multiply the terms with the same base by adding their exponents

\frac{x ^{2}}{4} x^{3 + 2} \times 24

Add the numbers

\frac{x ^{2}}{4} x^{5} \times 24

Multiply the terms

More Steps

Multiply the terms

\frac{x ^{2}}{4} x^{5}

Multiply the terms

\frac{x ^{2} \times x ^{5}}{4}

Multiply the terms

\frac{x ^{7}}{4}

\frac{x ^{7}}{4} \times 24

Cancel out the common factor 4

x^{7} \times 6

Use the commutative property to reorder the terms

6 x^{7}

(x - 2 x^{5}) \times 6 x^{7} = 0

Multiply the terms

6 x^{7} (x - 2 x^{5}) = 0

Elimination the left coefficient

x^{7} (x - 2 x^{5}) = 0

Separate the equation into 2 possible cases

x^{7} = 0 x - 2 x^{5} = 0

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

x = 0 x - 2 x^{5} = 0

Solve the equation

More Steps

Evaluate

x - 2 x^{5} = 0

Factor the expression

x (1 - 2 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 1 - 2 x^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 2 x^{4} = 0

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

- 2 x^{4} = 0 - 1

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

- 2 x^{4} = - 1

Change the signs on both sides of the equation

2 x^{4} = 1

Divide both sides

\frac{2 x ^{4}}{2} = \frac{1}{2}

Divide the numbers

x^{4} = \frac{1}{2}

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

x = \pm 4 \frac{1}{2}

Simplify the expression

x = \pm \frac{4 8}{2}

Separate the equation into 2 possible cases

x = \frac{4 8}{2} x = - \frac{4 8}{2}

x = 0 x = \frac{4 8}{2} x = - \frac{4 8}{2}

x = 0 x = 0 x = \frac{4 8}{2} x = - \frac{4 8}{2}

Find the union

x = 0 x = \frac{4 8}{2} x = - \frac{4 8}{2}

Solution

x_{1} = - \frac{4 8}{2}, x_{2} = 0, x_{3} = \frac{4 8}{2}

Alternative Form

x_{1} \approx - 0.840896, x_{2} = 0, x_{3} \approx 0.840896

Show Solution