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

Question

Simplify the expression

1 - 3 x + 2 x^{2}

Evaluate

(1 - x) (1 - 2 x)

Apply the distributive property

1 \times 1 - 1 \times 2 x - x \times 1 - (- x \times 2 x)

Any expression multiplied by 1 remains the same

1 - 1 \times 2 x - x \times 1 - (- x \times 2 x)

Any expression multiplied by 1 remains the same

1 - 2 x - x \times 1 - (- x \times 2 x)

Any expression multiplied by 1 remains the same

1 - 2 x - x - (- x \times 2 x)

Multiply the terms

More Steps

Evaluate

- x \times 2 x

Multiply the numbers

- 2 x \times x

Multiply the terms

- 2 x^{2}

1 - 2 x - x - (- 2 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

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

Solution

More Steps

Evaluate

- 2 x - x

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

(- 2 - 1) x

Subtract the numbers

- 3 x

1 - 3 x + 2 x^{2}

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

(1 - x) (1 - 2 x)

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

(1 - x) (1 - 2 x) = 0

Separate the equation into 2 possible cases

1 - x = 0 1 - 2 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 = 1 1 - 2 x = 0

Solve the equation

More Steps

Evaluate

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

Solution

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

Alternative Form

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

Show Solution