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

Question

Simplify the expression

n^{7} - 9 n^{6} + 34 n^{5} - 70 n^{4} + 85 n^{3} - 61 n^{2} + 24 n - 4

Evaluate

(n - 1)^{2} (n - 1)^{3} (n - 2)^{2}

Multiply the terms with the same base by adding their exponents

(n - 1)^{2 + 3} (n - 2)^{2}

Add the numbers

(n - 1)^{5} (n - 2)^{2}

Expand the expression

(n^{5} - 5 n^{4} + 10 n^{3} - 10 n^{2} + 5 n - 1) (n - 2)^{2}

Expand the expression

More Steps

(n^{5} - 5 n^{4} + 10 n^{3} - 10 n^{2} + 5 n - 1) (n^{2} - 4 n + 4)

Apply the distributive property

n^{5} \times n^{2} - n^{5} \times 4 n + n^{5} \times 4 - 5 n^{4} \times n^{2} - (- 5 n^{4} \times 4 n) - 5 n^{4} \times 4 + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - n^{5} \times 4 n + n^{5} \times 4 - 5 n^{4} \times n^{2} - (- 5 n^{4} \times 4 n) - 5 n^{4} \times 4 + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + n^{5} \times 4 - 5 n^{4} \times n^{2} - (- 5 n^{4} \times 4 n) - 5 n^{4} \times 4 + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Use the commutative property to reorder the terms

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{4} \times n^{2} - (- 5 n^{4} \times 4 n) - 5 n^{4} \times 4 + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 5 n^{4} \times 4 n) - 5 n^{4} \times 4 + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 5 n^{4} \times 4 + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the numbers

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{3} \times n^{2} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 10 n^{3} \times 4 n + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 10 n^{3} \times 4 - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the numbers

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{2} \times n^{2} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} - (- 10 n^{2} \times 4 n) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} - (- 40 n^{3}) - 10 n^{2} \times 4 + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the numbers

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} - (- 40 n^{3}) - 40 n^{2} + 5 n \times n^{2} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} - (- 40 n^{3}) - 40 n^{2} + 5 n^{3} - 5 n \times 4 n + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the terms

More Steps

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} - (- 40 n^{3}) - 40 n^{2} + 5 n^{3} - 20 n^{2} + 5 n \times 4 - n^{2} - (- 4 n) - 4

Multiply the numbers

n^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} - (- 20 n^{5}) - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} - (- 40 n^{3}) - 40 n^{2} + 5 n^{3} - 20 n^{2} + 20 n - n^{2} - (- 4 n) - 4

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^{7} - 4 n^{6} + 4 n^{5} - 5 n^{6} + 20 n^{5} - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} + 40 n^{3} - 40 n^{2} + 5 n^{3} - 20 n^{2} + 20 n - n^{2} + 4 n - 4

Subtract the terms

More Steps

n^{7} - 9 n^{6} + 4 n^{5} + 20 n^{5} - 20 n^{4} + 10 n^{5} - 40 n^{4} + 40 n^{3} - 10 n^{4} + 40 n^{3} - 40 n^{2} + 5 n^{3} - 20 n^{2} + 20 n - n^{2} + 4 n - 4

Add the terms

More Steps

n^{7} - 9 n^{6} + 34 n^{5} - 20 n^{4} - 40 n^{4} + 40 n^{3} - 10 n^{4} + 40 n^{3} - 40 n^{2} + 5 n^{3} - 20 n^{2} + 20 n - n^{2} + 4 n - 4

Subtract the terms

More Steps

n^{7} - 9 n^{6} + 34 n^{5} - 70 n^{4} + 40 n^{3} + 40 n^{3} - 40 n^{2} + 5 n^{3} - 20 n^{2} + 20 n - n^{2} + 4 n - 4

Add the terms

More Steps

n^{7} - 9 n^{6} + 34 n^{5} - 70 n^{4} + 85 n^{3} - 40 n^{2} - 20 n^{2} + 20 n - n^{2} + 4 n - 4

Subtract the terms

More Steps

n^{7} - 9 n^{6} + 34 n^{5} - 70 n^{4} + 85 n^{3} - 61 n^{2} + 20 n + 4 n - 4

Solution

More Steps

n^{7} - 9 n^{6} + 34 n^{5} - 70 n^{4} + 85 n^{3} - 61 n^{2} + 24 n - 4

Show Solution

Find the roots

n_{1} = 1, n_{2} = 2

Show Solution