Solve x^34x^22x-8

Question

Simplify the expression

8 x^{6} - 8

Evaluate

x^{3} \times 4 x^{2} \times 2 x - 8

Solution

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Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2 + 1} \times 4 \times 2

Add the numbers

x^{6} \times 4 \times 2

Multiply the terms

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

8 x^{6} - 8

Show Solution

Factor the expression

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

Evaluate

x^{3} \times 4 x^{2} \times 2 x - 8

Evaluate

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Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2 + 1} \times 4 \times 2

Add the numbers

x^{6} \times 4 \times 2

Multiply the terms

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

8 x^{6} - 8

Factor out 8 from the expression

8 (x^{6} - 1)

Factor the expression

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Evaluate

x^{6} - 1

Rewrite the expression in exponential form

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

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

8 (x^{3} - 1) (x^{3} + 1)

Evaluate

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Evaluate

x^{3} - 1

Rewrite the expression in exponential form

x^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

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

Any expression multiplied by 1 remains the same

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

1 raised to any power equals to 1

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

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

Solution

More Steps

Evaluate

x^{3} + 1

Rewrite the expression in exponential form

x^{3} + 1^{3}

Use a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) to factor the expression

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

Any expression multiplied by 1 remains the same

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

1 raised to any power equals to 1

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

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

Show Solution

Find the roots

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

Evaluate

x^{3} \times 4 x^{2} \times 2 x - 8

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

x^{3} \times 4 x^{2} \times 2 x - 8 = 0

Multiply

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Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2 + 1} \times 4 \times 2

Add the numbers

x^{6} \times 4 \times 2

Multiply the terms

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

8 x^{6} - 8 = 0

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

8 x^{6} = 0 + 8

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

8 x^{6} = 8

Divide both sides

\frac{8 x ^{6}}{8} = \frac{8}{8}

Divide the numbers

x^{6} = \frac{8}{8}

Divide the numbers

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Evaluate

\frac{8}{8}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{6} = 1

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

x = \pm 61

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

Solution

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

Show Solution