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

Question

Simplify the expression

x^{3} - 7 x^{2} + 15 x - 9

Evaluate

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

Expand the expression

More Steps

Evaluate

(x - 3)^{2}

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

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

Calculate

x^{2} - 6 x + 9

(x - 1) (x^{2} - 6 x + 9)

Apply the distributive property

x \times x^{2} - x \times 6 x + x \times 9 - x^{2} - (- 6 x) - 9

Multiply the terms

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Evaluate

x \times x^{2}

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

x^{1 + 2}

Add the numbers

x^{3}

x^{3} - x \times 6 x + x \times 9 - x^{2} - (- 6 x) - 9

Multiply the terms

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Evaluate

x \times 6 x

Use the commutative property to reorder the terms

6 x \times x

Multiply the terms

6 x^{2}

x^{3} - 6 x^{2} + x \times 9 - x^{2} - (- 6 x) - 9

Use the commutative property to reorder the terms

x^{3} - 6 x^{2} + 9 x - x^{2} - (- 6 x) - 9

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} + 9 x - x^{2} + 6 x - 9

Subtract the terms

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Evaluate

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

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

(- 6 - 1) x^{2}

Subtract the numbers

- 7 x^{2}

x^{3} - 7 x^{2} + 9 x + 6 x - 9

Solution

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Evaluate

9 x + 6 x

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

(9 + 6) x

Add the numbers

15 x

x^{3} - 7 x^{2} + 15 x - 9

Show Solution

Find the roots

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

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

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

Solve the equation

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Evaluate

(x - 3)^{2} = 0

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

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 1 x = 3

Solution

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

Show Solution