Solve (x^2 4x-12)(x^3)

Question

Simplify the expression

4 x^{6} - 12 x^{3}

Evaluate

(x^{2} \times 4 x - 12) x^{3}

Multiply

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Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

(4 x^{3} - 12) x^{3}

Multiply the terms

x^{3} (4 x^{3} - 12)

Apply the distributive property

x^{3} \times 4 x^{3} - x^{3} \times 12

Multiply the terms

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Evaluate

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

Use the commutative property to reorder the terms

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

Multiply the terms

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Evaluate

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

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

x^{3 + 3}

Add the numbers

x^{6}

4 x^{6}

4 x^{6} - x^{3} \times 12

Solution

4 x^{6} - 12 x^{3}

Show Solution

Factor the expression

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

Evaluate

(x^{2} \times 4 x - 12) x^{3}

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

(4 x^{3} - 12) x^{3}

Multiply the terms

x^{3} (4 x^{3} - 12)

Factor the expression

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

Solution

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

Show Solution

Find the roots

x_{1} = 0, x_{2} = 33

Alternative Form

x_{1} = 0, x_{2} \approx 1.44225

Evaluate

(x^{2} \times 4 x - 12) (x^{3})

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

(x^{2} \times 4 x - 12) (x^{3}) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

(4 x^{3} - 12) (x^{3}) = 0

Calculate

(4 x^{3} - 12) x^{3} = 0

Multiply the terms

x^{3} (4 x^{3} - 12) = 0

Separate the equation into 2 possible cases

x^{3} = 0 4 x^{3} - 12 = 0

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

x = 0 4 x^{3} - 12 = 0

Solve the equation

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Evaluate

4 x^{3} - 12 = 0

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

4 x^{3} = 0 + 12

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

4 x^{3} = 12

Divide both sides

\frac{4 x ^{3}}{4} = \frac{12}{4}

Divide the numbers

x^{3} = \frac{12}{4}

Divide the numbers

More Steps

Evaluate

\frac{12}{4}

Reduce the numbers

\frac{3}{1}

Calculate

3

x^{3} = 3

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

3 x^{3} = 33

Calculate

x = 33

x = 0 x = 33

Solution

x_{1} = 0, x_{2} = 33

Alternative Form

x_{1} = 0, x_{2} \approx 1.44225

Show Solution