Solve (4x-4) (-x-1)

Question

Simplify the expression

- 4 x^{2} + 4

Evaluate

(4 x - 4) (- x - 1)

Apply the distributive property

4 x (- x) - 4 x \times 1 - 4 (- x) - (- 4 \times 1)

Multiply the terms

More Steps

Evaluate

4 x (- x)

Multiply the numbers

- 4 x \times x

Multiply the terms

- 4 x^{2}

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

Any expression multiplied by 1 remains the same

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

Multiply the numbers

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

Any expression multiplied by 1 remains the same

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

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

The sum of two opposites equals 0

More Steps

Evaluate

- 4 x + 4 x

Collect like terms

(- 4 + 4) x

Add the coefficients

0 \times x

Calculate

0

- 4 x^{2} + 0 + 4

Solution

- 4 x^{2} + 4

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Factor the expression

- 4 (x - 1) (x + 1)

Evaluate

(4 x - 4) (- x - 1)

Factor the expression

4 (x - 1) (- x - 1)

Factor the expression

4 (x - 1) (- 1) (x + 1)

Solution

- 4 (x - 1) (x + 1)

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Find the roots

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

Evaluate

(4 x - 4) (- x - 1)

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

(4 x - 4) (- x - 1) = 0

Separate the equation into 2 possible cases

4 x - 4 = 0 - x - 1 = 0

Solve the equation

More Steps

Evaluate

4 x - 4 = 0

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

4 x = 0 + 4

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

4 x = 4

Divide both sides

\frac{4 x}{4} = \frac{4}{4}

Divide the numbers

x = \frac{4}{4}

Divide the numbers

More Steps

Evaluate

\frac{4}{4}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

x = 1 - x - 1 = 0

Solve the equation

More Steps

Evaluate

- x - 1 = 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 x = - 1

Solution

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

Show Solution