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

Question

Simplify the expression

x^{3} - 4 x^{2} + 5 x - 2

Evaluate

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

Multiply the first two terms

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

Expand the expression

More Steps

Evaluate

(x - 1)^{2}

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

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

Calculate

x^{2} - 2 x + 1

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

Apply the distributive property

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

x^{3} - 2 x^{2} - 2 x^{2} - (- 4 x) + 1 \times x - 1 \times 2

Any expression multiplied by 1 remains the same

x^{3} - 2 x^{2} - 2 x^{2} - (- 4 x) + x - 1 \times 2

Any expression multiplied by 1 remains the same

x^{3} - 2 x^{2} - 2 x^{2} - (- 4 x) + x - 2

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} - 2 x^{2} + 4 x + x - 2

Subtract the terms

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Evaluate

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

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

(- 2 - 2) x^{2}

Subtract the numbers

- 4 x^{2}

x^{3} - 4 x^{2} + 4 x + x - 2

Solution

More Steps

Evaluate

4 x + x

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

(4 + 1) x

Add the numbers

5 x

x^{3} - 4 x^{2} + 5 x - 2

Show Solution

Find the roots

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

Evaluate

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

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

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

Multiply the first two terms

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

(x - 1)^{2} = 0

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

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 = 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 = 1 x = 2

Solution

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

Show Solution