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

Question

Simplify the expression

5 x^{2} - x^{3} - 8 x + 4

Evaluate

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

Expand the expression

More Steps

Evaluate

(x - 2)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

x^{2} - 2 x \times 2 + 2^{2}

Calculate

x^{2} - 4 x + 4

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

Apply the distributive property

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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

Add the terms

More Steps

Evaluate

x^{2} + 4 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 4) x^{2}

Add the numbers

5 x^{2}

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

Solution

More Steps

Evaluate

- 4 x - 4 x

Collect like terms by calculating the sum or difference of their coefficients

(- 4 - 4) x

Subtract the numbers

- 8 x

5 x^{2} - x^{3} - 8 x + 4

Show Solution

Find the roots

x_{1} = 1, x_{2} = 2

Evaluate

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

To find the roots of the expression,set the expression equal to 0

(x - 2)^{2} (1 - x) = 0

Separate the equation into 2 possible cases

(x - 2)^{2} = 0 1 - x = 0

Solve the equation

More Steps

Evaluate

(x - 2)^{2} = 0

The only way a power can be 0 is when the base equals 0

x - 2 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

x = 2

x = 2 1 - x = 0

Solve the equation

More Steps

Evaluate

1 - x = 0

Move the constant to the right-hand side and change its sign

- x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- x = - 1

Change the signs on both sides of the equation

x = 1

x = 2 x = 1

Solution

x_{1} = 1, x_{2} = 2

Show Solution