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

Evaluate

(x - 2) (x - 1)^{3} (x \times 1)^{2} (x - 2)

Any expression multiplied by 1 remains the same

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

Use the commutative property to reorder the terms

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

Multiply the terms

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

Expand the expression

More Steps

(x^{2} - 4 x + 4) x^{2} (x - 1)^{3}

Expand the expression

More Steps

(x^{2} - 4 x + 4) x^{2} (x^{3} - 3 x^{2} + 3 x - 1)

Multiply the terms

More Steps

(x^{4} - 4 x^{3} + 4 x^{2}) (x^{3} - 3 x^{2} + 3 x - 1)

Apply the distributive property

x^{4} \times x^{3} - x^{4} \times 3 x^{2} + x^{4} \times 3 x - x^{4} \times 1 - 4 x^{3} \times x^{3} - (- 4 x^{3} \times 3 x^{2}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - x^{4} \times 3 x^{2} + x^{4} \times 3 x - x^{4} \times 1 - 4 x^{3} \times x^{3} - (- 4 x^{3} \times 3 x^{2}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + x^{4} \times 3 x - x^{4} \times 1 - 4 x^{3} \times x^{3} - (- 4 x^{3} \times 3 x^{2}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} \times 1 - 4 x^{3} \times x^{3} - (- 4 x^{3} \times 3 x^{2}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Any expression multiplied by 1 remains the same

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{3} \times x^{3} - (- 4 x^{3} \times 3 x^{2}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 4 x^{3} \times 3 x^{2}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 4 x^{3} \times 3 x - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 12 x^{4} - (- 4 x^{3} \times 1) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Any expression multiplied by 1 remains the same

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 12 x^{4} - (- 4 x^{3}) + 4 x^{2} \times x^{3} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 12 x^{4} - (- 4 x^{3}) + 4 x^{5} - 4 x^{2} \times 3 x^{2} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 12 x^{4} - (- 4 x^{3}) + 4 x^{5} - 12 x^{4} + 4 x^{2} \times 3 x - 4 x^{2} \times 1

Multiply the terms

More Steps

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 12 x^{4} - (- 4 x^{3}) + 4 x^{5} - 12 x^{4} + 12 x^{3} - 4 x^{2} \times 1

Any expression multiplied by 1 remains the same

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} - (- 12 x^{5}) - 12 x^{4} - (- 4 x^{3}) + 4 x^{5} - 12 x^{4} + 12 x^{3} - 4 x^{2}

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

x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 4 x^{6} + 12 x^{5} - 12 x^{4} + 4 x^{3} + 4 x^{5} - 12 x^{4} + 12 x^{3} - 4 x^{2}

Subtract the terms

More Steps

x^{7} - 7 x^{6} + 3 x^{5} - x^{4} + 12 x^{5} - 12 x^{4} + 4 x^{3} + 4 x^{5} - 12 x^{4} + 12 x^{3} - 4 x^{2}

Add the terms

More Steps

x^{7} - 7 x^{6} + 19 x^{5} - x^{4} - 12 x^{4} + 4 x^{3} - 12 x^{4} + 12 x^{3} - 4 x^{2}

Subtract the terms

More Steps

x^{7} - 7 x^{6} + 19 x^{5} - 25 x^{4} + 4 x^{3} + 12 x^{3} - 4 x^{2}

Solution

More Steps

x^{7} - 7 x^{6} + 19 x^{5} - 25 x^{4} + 16 x^{3} - 4 x^{2}

Simplify the expression

Find the roots