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

Question

Simplify the expression

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

Evaluate

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

Multiply

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Evaluate

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}

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

Apply the distributive property

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

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 4

Solution

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

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Factor the expression

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

Evaluate

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

Multiply

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Evaluate

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}

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

Factor the expression

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Evaluate

4 x^{3} - 4

Factor out 4 from the expression

4 (x^{3} - 1)

Factor the expression

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Evaluate

x^{3} - 1

Calculate

x^{3} + x^{2} + x - x^{2} - x - 1

Rewrite the expression

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

Factor out x from the expression

x (x^{2} + x + 1) - x^{2} - x - 1

Factor out - 1 from the expression

x (x^{2} + x + 1) - (x^{2} + x + 1)

Factor out x^{2} + x + 1 from the expression

(x - 1) (x^{2} + x + 1)

4 (x - 1) (x^{2} + x + 1)

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

Solution

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

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Find the roots

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

Evaluate

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

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

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

Calculate

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

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}

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

4 x^{3} - 4 = 0

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

4 x^{3} = 0 + 4

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

4 x^{3} = 4

Divide both sides

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

Divide the numbers

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

Divide the numbers

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Evaluate

\frac{4}{4}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{3} = 1

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

3 x^{3} = 31

Calculate

x = 31

Simplify the root

x = 1

x = 0 x = 1

Solution

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

Show Solution