Solve (n-2010)(n-2011)(n-2012)

Question

Simplify the expression

n^{3} - 6033 n^{2} + 12132362 n - 8132725320

Evaluate

(n - 2010) (n - 2011) (n - 2012)

Multiply the terms

More Steps

(n^{2} - 4021 n + 4042110) (n - 2012)

Apply the distributive property

n^{2} \times n - n^{2} \times 2012 - 4021 n \times n - (- 4021 n \times 2012) + 4042110 n - 4042110 \times 2012

Multiply the terms

More Steps

n^{3} - n^{2} \times 2012 - 4021 n \times n - (- 4021 n \times 2012) + 4042110 n - 4042110 \times 2012

Use the commutative property to reorder the terms

n^{3} - 2012 n^{2} - 4021 n \times n - (- 4021 n \times 2012) + 4042110 n - 4042110 \times 2012

Multiply the terms

n^{3} - 2012 n^{2} - 4021 n^{2} - (- 4021 n \times 2012) + 4042110 n - 4042110 \times 2012

Multiply the numbers

n^{3} - 2012 n^{2} - 4021 n^{2} - (- 8090252 n) + 4042110 n - 4042110 \times 2012

Multiply the numbers

n^{3} - 2012 n^{2} - 4021 n^{2} - (- 8090252 n) + 4042110 n - 8132725320

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} - 2012 n^{2} - 4021 n^{2} + 8090252 n + 4042110 n - 8132725320

Subtract the terms

More Steps

n^{3} - 6033 n^{2} + 8090252 n + 4042110 n - 8132725320

Solution

More Steps

n^{3} - 6033 n^{2} + 12132362 n - 8132725320

Show Solution

Find the roots

n_{1} = 2010, n_{2} = 2011, n_{3} = 2012

Show Solution