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

Question

Simplify the expression

192 x^{10} - 32 x^{12}

Evaluate

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

Remove the parentheses

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

Multiply the terms

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Evaluate

2 \times 4 \times 4

Multiply the terms

8 \times 4

Multiply the numbers

32

(6 x - x^{3}) \times 32 x^{2} \times x^{3} \times x^{3} \times x

Multiply the terms with the same base by adding their exponents

(6 x - x^{3}) \times 32 x^{2 + 3 + 3 + 1}

Add the numbers

(6 x - x^{3}) \times 32 x^{9}

Multiply the terms

32 x^{9} (6 x - x^{3})

Apply the distributive property

32 x^{9} \times 6 x - 32 x^{9} \times x^{3}

Multiply the terms

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Evaluate

32 x^{9} \times 6 x

Multiply the numbers

192 x^{9} \times x

Multiply the terms

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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}

192 x^{10}

192 x^{10} - 32 x^{9} \times x^{3}

Solution

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Evaluate

x^{9} \times x^{3}

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

x^{9 + 3}

Add the numbers

x^{12}

192 x^{10} - 32 x^{12}

Show Solution

Factor the expression

32 x^{10} (6 - x^{2})

Evaluate

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

Remove the parentheses

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

Multiply

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Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{2 + 3}

Add the numbers

2 x^{5}

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

Multiply

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Multiply the terms

4 x^{3} \times 4 x

Multiply the terms

16 x^{3} \times x

Multiply the terms with the same base by adding their exponents

16 x^{3 + 1}

Add the numbers

16 x^{4}

(6 x - x^{3}) \times 2 x^{5} \times 16 x^{4}

Multiply the terms

(6 x - x^{3}) \times 32 x^{5} \times x^{4}

Multiply the terms with the same base by adding their exponents

(6 x - x^{3}) \times 32 x^{5 + 4}

Add the numbers

(6 x - x^{3}) \times 32 x^{9}

Multiply the terms

32 x^{9} (6 x - x^{3})

Factor the expression

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Evaluate

6 x - x^{3}

Rewrite the expression

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

Factor out x from the expression

x (6 - x^{2})

32 x^{9} \times x (6 - x^{2})

Solution

32 x^{10} (6 - x^{2})

Show Solution

Find the roots

x_{1} = - 6, x_{2} = 0, x_{3} = 6

Alternative Form

x_{1} \approx - 2.44949, x_{2} = 0, x_{3} \approx 2.44949

Evaluate

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

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

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

Multiply

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Multiply the terms

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

Multiply the terms with the same base by adding their exponents

2 x^{2 + 3}

Add the numbers

2 x^{5}

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

Multiply

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Multiply the terms

4 x^{3} \times 4 x

Multiply the terms

16 x^{3} \times x

Multiply the terms with the same base by adding their exponents

16 x^{3 + 1}

Add the numbers

16 x^{4}

(6 x - x^{3}) \times 2 x^{5} \times 16 x^{4} = 0

Multiply the terms

More Steps

Multiply the terms

(6 x - x^{3}) \times 2 x^{5} \times 16 x^{4}

Multiply the terms

(6 x - x^{3}) \times 32 x^{5} \times x^{4}

Multiply the terms with the same base by adding their exponents

(6 x - x^{3}) \times 32 x^{5 + 4}

Add the numbers

(6 x - x^{3}) \times 32 x^{9}

Multiply the terms

32 x^{9} (6 x - x^{3})

32 x^{9} (6 x - x^{3}) = 0

Elimination the left coefficient

x^{9} (6 x - x^{3}) = 0

Separate the equation into 2 possible cases

x^{9} = 0 6 x - x^{3} = 0

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

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

Solve the equation

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Evaluate

6 x - x^{3} = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

6 - x^{2} = 0

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

- x^{2} = 0 - 6

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

- x^{2} = - 6

Change the signs on both sides of the equation

x^{2} = 6

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

x = \pm 6

Separate the equation into 2 possible cases

x = 6 x = - 6

x = 0 x = 6 x = - 6

x = 0 x = 0 x = 6 x = - 6

Find the union

x = 0 x = 6 x = - 6

Solution

x_{1} = - 6, x_{2} = 0, x_{3} = 6

Alternative Form

x_{1} \approx - 2.44949, x_{2} = 0, x_{3} \approx 2.44949

Show Solution