Solve -4(x-1)(x-3)

Question

Simplify the expression

- 4 x^{2} + 16 x - 12

Evaluate

- 4 (x - 1) (x - 3)

Multiply the terms

More Steps

Evaluate

- 4 (x - 1)

Apply the distributive property

- 4 x - (- 4 \times 1)

Any expression multiplied by 1 remains the same

- 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 + 4

(- 4 x + 4) (x - 3)

Apply the distributive property

- 4 x \times x - (- 4 x \times 3) + 4 x - 4 \times 3

Multiply the terms

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

Multiply the numbers

- 4 x^{2} - (- 12 x) + 4 x - 4 \times 3

Multiply the numbers

- 4 x^{2} - (- 12 x) + 4 x - 12

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} + 12 x + 4 x - 12

Solution

More Steps

Evaluate

12 x + 4 x

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

(12 + 4) x

Add the numbers

16 x

- 4 x^{2} + 16 x - 12

Show Solution

Find the roots

x_{1} = 1, x_{2} = 3

Evaluate

- 4 (x - 1) (x - 3)

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

- 4 (x - 1) (x - 3) = 0

Change the sign

4 (x - 1) (x - 3) = 0

Elimination the left coefficient

(x - 1) (x - 3) = 0

Separate the equation into 2 possible cases

x - 1 = 0 x - 3 = 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

x = 1 x - 3 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 1 x = 3

Solution

x_{1} = 1, x_{2} = 3

Show Solution