Solve k(k-1)^2(k-2)

Question

Simplify the expression

k^{4} - 4 k^{3} + 5 k^{2} - 2 k

Evaluate

k (k - 1)^{2} (k - 2)

Expand the expression

More Steps

k (k^{2} - 2 k + 1) (k - 2)

Multiply the terms

More Steps

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

Apply the distributive property

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

Multiply the terms

More Steps

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

Use the commutative property to reorder the terms

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

Multiply the terms

More Steps

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

Multiply the numbers

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Subtract the terms

More Steps

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

Solution

More Steps

k^{4} - 4 k^{3} + 5 k^{2} - 2 k

Show Solution

Find the roots

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

Show Solution