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

Question

Simplify the expression

x^{12} - x^{3}

Evaluate

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

Multiply the terms

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Multiply the terms

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 3}

Add the numbers

x^{6}

(x^{6})^{2} - x^{3}

Solution

More Steps

Evaluate

(x^{6})^{2}

Transform the expression

x^{6 \times 2}

Multiply the numbers

x^{12}

x^{12} - x^{3}

Show Solution

Factor the expression

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

Evaluate

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

Evaluate

More Steps

Evaluate

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

Multiply the terms

More Steps

Multiply the terms

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 3}

Add the numbers

x^{6}

(x^{6})^{2}

Transform the expression

x^{6 \times 2}

Multiply the numbers

x^{12}

x^{12} - x^{3}

Factor out x^{3} from the expression

x^{3} (x^{9} - 1)

Factor the expression

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Evaluate

x^{9} - 1

Rewrite the expression in exponential form

x^{9} - 1^{3}

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

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

Any expression multiplied by 1 remains the same

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

1 raised to any power equals to 1

(x^{3} - 1) (x^{6} + x^{3} + 1)

x^{3} (x^{3} - 1) (x^{6} + 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)

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

Show Solution

Find the roots

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

Evaluate

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

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

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

Multiply the terms

More Steps

Multiply the terms

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

x^{1 + 2 + 3}

Add the numbers

x^{6}

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

Evaluate the power

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Evaluate

(x^{6})^{2}

Transform the expression

x^{6 \times 2}

Multiply the numbers

x^{12}

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

Factor the expression

x^{3} (x^{9} - 1) = 0

Separate the equation into 2 possible cases

x^{3} = 0 x^{9} - 1 = 0

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

x = 0 x^{9} - 1 = 0

Solve the equation

More Steps

Evaluate

x^{9} - 1 = 0

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

x^{9} = 0 + 1

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

x^{9} = 1

Take the 9 -th root on both sides of the equation

9 x^{9} = 91

Calculate

x = 91

Simplify the root

x = 1

x = 0 x = 1

Solution

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

Show Solution