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

Question

Simplify the expression

3 x^{2} - 3 x + 1

Evaluate

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

Expand the expression

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

The sum of two opposites equals 0

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Evaluate

x^{3} - x^{3}

Collect like terms

(1 - 1) x^{3}

Add the coefficients

0 \times x^{3}

Calculate

0

0 + 3 x^{2} - 3 x + 1

Solution

3 x^{2} - 3 x + 1

Show Solution

Factor the expression

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

Evaluate

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

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

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

Calculate

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Simplify

x - x + 1

The sum of two opposites equals 0

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Evaluate

x - x

Collect like terms

(1 - 1) x

Add the coefficients

0 \times x

Calculate

0

0 + 1

Remove 0

1

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

Solution

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Simplify

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

Simplify

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Simplify

x (x - 1)

Apply the distributive property

x \times x + x (- 1)

Multiply the terms

x^{2} + x (- 1)

Multiplying or dividing an odd number of negative terms equals a negative

x^{2} - x

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

Simplify

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Evaluate

x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 1) x^{2}

Add the numbers

2 x^{2}

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

Expand the expression

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

Add the terms

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Evaluate

2 x^{2} + x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(2 + 1) x^{2}

Add the numbers

3 x^{2}

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

Subtract the terms

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Evaluate

- x - 2 x

Collect like terms by calculating the sum or difference of their coefficients

(- 1 - 2) x

Subtract the numbers

- 3 x

3 x^{2} - 3 x + 1

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

Show Solution

Find the roots

x_{1} = \frac{1}{2} - \frac{3}{6} i, x_{2} = \frac{1}{2} + \frac{3}{6} i

Alternative Form

x_{1} \approx 0.5 - 0.288675 i, x_{2} \approx 0.5 + 0.288675 i

Evaluate

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

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

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

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

(x - x + 1) (x^{2} + x (x - 1) + (x - 1)^{2}) = 0

Separate the equation into 2 possible cases

x - x + 1 = 0 x^{2} + x (x - 1) + (x - 1)^{2} = 0

Solve the equation

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Evaluate

x - x + 1 = 0

Calculate the sum or difference

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Evaluate

x - x + 1

The sum of two opposites equals 0

0 + 1

Remove 0

1

1 = 0

The statement is false for any value of x

x \in \emptyset

x \in \emptyset x^{2} + x (x - 1) + (x - 1)^{2} = 0

Solve the equation

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Evaluate

x^{2} + x (x - 1) + (x - 1)^{2} = 0

Calculate

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Evaluate

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

Expand the expression

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

Expand the expression

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

Add the terms

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

Subtract the terms

3 x^{2} - 3 x + 1

3 x^{2} - 3 x + 1 = 0

Substitute a= 3,b= - 3 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 3}{6}

Simplify the expression

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Evaluate

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

Multiply the numbers

(- 3)^{2} - 12

Rewrite the expression

3^{2} - 12

Evaluate the power

9 - 12

Subtract the numbers

- 3

x = \frac{3 \pm - 3}{6}

Simplify the radical expression

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Evaluate

- 3

Evaluate the power

3 \times - 1

Evaluate the power

3 \times i

x = \frac{3 \pm 3 \times i}{6}

Separate the equation into 2 possible cases

x = \frac{3 + 3 \times i}{6} x = \frac{3 - 3 \times i}{6}

Simplify the expression

x = \frac{1}{2} + \frac{3}{6} i x = \frac{3 - 3 \times i}{6}

Simplify the expression

x = \frac{1}{2} + \frac{3}{6} i x = \frac{1}{2} - \frac{3}{6} i

x \in \emptyset x = \frac{1}{2} + \frac{3}{6} i x = \frac{1}{2} - \frac{3}{6} i

Find the union

x = \frac{1}{2} + \frac{3}{6} i x = \frac{1}{2} - \frac{3}{6} i

Solution

x_{1} = \frac{1}{2} - \frac{3}{6} i, x_{2} = \frac{1}{2} + \frac{3}{6} i

Alternative Form

x_{1} \approx 0.5 - 0.288675 i, x_{2} \approx 0.5 + 0.288675 i

Show Solution