Solve n (n-1) (n-2) (n-3)

Question

Simplify the expression

n^{4} - 6 n^{3} + 11 n^{2} - 6 n

Evaluate

n (n - 1) (n - 2) (n - 3)

Multiply the terms

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

n^{4} - 3 n^{3} - 3 n^{3} - (- 9 n^{2}) + 2 n \times n - 2 n \times 3

Multiply the terms

n^{4} - 3 n^{3} - 3 n^{3} - (- 9 n^{2}) + 2 n^{2} - 2 n \times 3

Multiply the numbers

n^{4} - 3 n^{3} - 3 n^{3} - (- 9 n^{2}) + 2 n^{2} - 6 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^{4} - 3 n^{3} - 3 n^{3} + 9 n^{2} + 2 n^{2} - 6 n

Subtract the terms

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n^{4} - 6 n^{3} + 9 n^{2} + 2 n^{2} - 6 n

Solution

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n^{4} - 6 n^{3} + 11 n^{2} - 6 n

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Find the roots

n_{1} = 0, n_{2} = 1, n_{3} = 2, n_{4} = 3

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