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

Question

Simplify the expression

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

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

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

Multiply the numbers

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

Multiply the terms

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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}

6 x^{5}

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

Solution

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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}

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

Show Solution

Factor the expression

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

Evaluate

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

Remove the parentheses

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

Multiply the terms

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Evaluate

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

Rewrite the expression

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

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

Factor the expression

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Evaluate

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

Rewrite the expression

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

Factor out x^{2} from the expression

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

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

Solution

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

Show Solution

Find the roots

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

Alternative Form

x_{1} \approx - 1.732051, x_{2} = 0, x_{3} \approx 1.732051

Evaluate

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

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

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

Multiply the terms

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Multiply the terms

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

Rewrite the expression

x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2

Add the numbers

x^{3} \times 2

Use the commutative property to reorder the terms

2 x^{3}

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

3 - x^{2} = 0

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

- x^{2} = 0 - 3

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

- x^{2} = - 3

Change the signs on both sides of the equation

x^{2} = 3

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

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

x = 0 x = 3 x = - 3

x = 0 x = 0 x = 3 x = - 3

Find the union

x = 0 x = 3 x = - 3

Solution

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

Alternative Form

x_{1} \approx - 1.732051, x_{2} = 0, x_{3} \approx 1.732051

Show Solution