Solve (x-1)(x-1)(x-6)

Question

Simplify the expression

Solution

x^{3} - 8 x^{2} + 13 x - 6

Evaluate

(x - 1) (x - 1) (x - 6)

Multiply the first two terms

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

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 - 6)

Apply the distributive property

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

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 6 - 2 x \times x - (- 2 x \times 6) + 1 \times x - 1 \times 6

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

x^{3} - 6 x^{2} - 2 x^{2} - (- 12 x) + 1 \times x - 1 \times 6

Any expression multiplied by 1 remains the same

x^{3} - 6 x^{2} - 2 x^{2} - (- 12 x) + x - 1 \times 6

Any expression multiplied by 1 remains the same

x^{3} - 6 x^{2} - 2 x^{2} - (- 12 x) + x - 6

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} - 6 x^{2} - 2 x^{2} + 12 x + x - 6

Subtract the terms

More Steps

Evaluate

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

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

(- 6 - 2) x^{2}

Subtract the numbers

- 8 x^{2}

x^{3} - 8 x^{2} + 12 x + x - 6

Solution

More Steps

Evaluate

12 x + x

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

(12 + 1) x

Add the numbers

13 x

x^{3} - 8 x^{2} + 13 x - 6

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = 1, x_{2} = 6

Evaluate

(x - 1) (x - 1) (x - 6)

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

(x - 1) (x - 1) (x - 6) = 0

Multiply the first two terms

(x - 1)^{2} (x - 6) = 0

Separate the equation into 2 possible cases

(x - 1)^{2} = 0 x - 6 = 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 - 6 = 0

Solve the equation

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 1 x = 6

Solution

x_{1} = 1, x_{2} = 6

Show Solution

(x 1)(x 1)(x 6)

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression