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

Question

Simplify the expression

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

Evaluate

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

Subtract the terms

More Steps

Simplify

x^{2} - 3 x^{2}

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

(1 - 3) x^{2}

Subtract the numbers

- 2 x^{2}

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

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

Any expression multiplied by 1 remains the same

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

Solution

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

Show Solution

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

Evaluate

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

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

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

Subtract the terms

More Steps

Simplify

x^{2} - 3 x^{2}

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

(1 - 3) x^{2}

Subtract the numbers

- 2 x^{2}

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

Multiply the terms

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

Change the sign

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1

Solution

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

Show Solution