Solve k(k-1)(k-2)(k-3)

Question

Simplify the expression

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

Evaluate

k (k - 1) (k - 2) (k - 3)

Multiply the terms

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

Multiply the terms

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

Apply the distributive property

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Multiply the numbers

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

Multiply the terms

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

Multiply the numbers

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

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

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

Subtract the terms

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

Solution

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

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Find the roots

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

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