Solve k (k-1) (k-2) (k-3) (k-4)

Question

Simplify the expression

k^{5} - 10 k^{4} + 35 k^{3} - 50 k^{2} + 24 k

Evaluate

k (k - 1) (k - 2) (k - 3) (k - 4)

Multiply the terms

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(k^{2} - k) (k - 2) (k - 3) (k - 4)

Multiply the terms

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

Multiply the terms

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

Apply the distributive property

k^{4} \times k - k^{4} \times 4 - 6 k^{3} \times k - (- 6 k^{3} \times 4) + 11 k^{2} \times k - 11 k^{2} \times 4 - 6 k \times k - (- 6 k \times 4)

Multiply the terms

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k^{5} - k^{4} \times 4 - 6 k^{3} \times k - (- 6 k^{3} \times 4) + 11 k^{2} \times k - 11 k^{2} \times 4 - 6 k \times k - (- 6 k \times 4)

Use the commutative property to reorder the terms

k^{5} - 4 k^{4} - 6 k^{3} \times k - (- 6 k^{3} \times 4) + 11 k^{2} \times k - 11 k^{2} \times 4 - 6 k \times k - (- 6 k \times 4)

Multiply the terms

More Steps

k^{5} - 4 k^{4} - 6 k^{4} - (- 6 k^{3} \times 4) + 11 k^{2} \times k - 11 k^{2} \times 4 - 6 k \times k - (- 6 k \times 4)

Multiply the numbers

k^{5} - 4 k^{4} - 6 k^{4} - (- 24 k^{3}) + 11 k^{2} \times k - 11 k^{2} \times 4 - 6 k \times k - (- 6 k \times 4)

Multiply the terms

More Steps

k^{5} - 4 k^{4} - 6 k^{4} - (- 24 k^{3}) + 11 k^{3} - 11 k^{2} \times 4 - 6 k \times k - (- 6 k \times 4)

Multiply the numbers

k^{5} - 4 k^{4} - 6 k^{4} - (- 24 k^{3}) + 11 k^{3} - 44 k^{2} - 6 k \times k - (- 6 k \times 4)

Multiply the terms

k^{5} - 4 k^{4} - 6 k^{4} - (- 24 k^{3}) + 11 k^{3} - 44 k^{2} - 6 k^{2} - (- 6 k \times 4)

Multiply the numbers

k^{5} - 4 k^{4} - 6 k^{4} - (- 24 k^{3}) + 11 k^{3} - 44 k^{2} - 6 k^{2} - (- 24 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^{5} - 4 k^{4} - 6 k^{4} + 24 k^{3} + 11 k^{3} - 44 k^{2} - 6 k^{2} + 24 k

Subtract the terms

More Steps

k^{5} - 10 k^{4} + 24 k^{3} + 11 k^{3} - 44 k^{2} - 6 k^{2} + 24 k

Add the terms

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k^{5} - 10 k^{4} + 35 k^{3} - 44 k^{2} - 6 k^{2} + 24 k

Solution

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k^{5} - 10 k^{4} + 35 k^{3} - 50 k^{2} + 24 k

Show Solution

Find the roots

k_{1} = 0, k_{2} = 1, k_{3} = 2, k_{4} = 3, k_{5} = 4

Show Solution