Solve (x 1)(x-1)(x-2)

Question

Simplify the expression

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

Evaluate

(x \times 1) (x - 1) (x - 2)

Remove the parentheses

x \times 1 \times (x - 1) (x - 2)

Any expression multiplied by 1 remains the same

x (x - 1) (x - 2)

Multiply the terms

More Steps

Evaluate

x (x - 1)

Apply the distributive property

x \times x - x \times 1

Multiply the terms

x^{2} - x \times 1

Any expression multiplied by 1 remains the same

x^{2} - x

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

Apply the distributive property

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

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}

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Solution

More Steps

Evaluate

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

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

(- 2 - 1) x^{2}

Subtract the numbers

- 3 x^{2}

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

Show Solution

Find the roots

x_{1} = 0, x_{2} = 1, x_{3} = 2

Evaluate

(x \times 1) (x - 1) (x - 2)

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

(x \times 1) (x - 1) (x - 2) = 0

Any expression multiplied by 1 remains the same

x (x - 1) (x - 2) = 0

Separate the equation into 3 possible cases

x = 0 x - 1 = 0 x - 2 = 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 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 1 x = 2

Solution

x_{1} = 0, x_{2} = 1, x_{3} = 2

Show Solution