Solve n (n-1) (n-2)

Question

Simplify the expression

n^{3} - 3 n^{2} + 2 n

Evaluate

n (n - 1) (n - 2)

Multiply the terms

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Evaluate

n (n - 1)

Apply the distributive property

n \times n - n \times 1

Multiply the terms

n^{2} - n \times 1

Any expression multiplied by 1 remains the same

n^{2} - n

(n^{2} - n) (n - 2)

Apply the distributive property

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

Multiply the terms

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Evaluate

n^{2} \times n

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

n^{2 + 1}

Add the numbers

n^{3}

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

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

n^{3} - 2 n^{2} - n^{2} + 2 n

Solution

More Steps

Evaluate

- 2 n^{2} - n^{2}

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

(- 2 - 1) n^{2}

Subtract the numbers

- 3 n^{2}

n^{3} - 3 n^{2} + 2 n

Show Solution

Find the roots

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

Evaluate

n (n - 1) (n - 2)

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

n (n - 1) (n - 2) = 0

Separate the equation into 3 possible cases

n = 0 n - 1 = 0 n - 2 = 0

Solve the equation

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Evaluate

n - 1 = 0

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

n = 0 + 1

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

n = 1

n = 0 n = 1 n - 2 = 0

Solve the equation

More Steps

Evaluate

n - 2 = 0

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

n = 0 + 2

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

n = 2

n = 0 n = 1 n = 2

Solution

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

Show Solution