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

Question

Simplify the expression

1 - 5 x + 8 x^{2} - 4 x^{3}

Evaluate

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

Expand the expression

More Steps

Evaluate

(1 - 2 x)^{2}

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

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

Calculate

1 - 4 x + 4 x^{2}

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

Apply the distributive property

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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

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

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

Subtract the terms

More Steps

Evaluate

- x - 4 x

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

(- 1 - 4) x

Subtract the numbers

- 5 x

1 - 5 x + 4 x^{2} + 4 x^{2} - 4 x^{3}

Solution

More Steps

Evaluate

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

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

(4 + 4) x^{2}

Add the numbers

8 x^{2}

1 - 5 x + 8 x^{2} - 4 x^{3}

Show Solution

Find the roots

x_{1} = \frac{1}{2}, x_{2} = 1

Alternative Form

x_{1} = 0.5, x_{2} = 1

Evaluate

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

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

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

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

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

1 - 2 x = 0

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

- 2 x = 0 - 1

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

- 2 x = - 1

Change the signs on both sides of the equation

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{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 = \frac{1}{2} x = 1

Solution

x_{1} = \frac{1}{2}, x_{2} = 1

Alternative Form

x_{1} = 0.5, x_{2} = 1

Show Solution