Solve 2(x-1)(x-3)

Question

Simplify the expression

2 x^{2} - 8 x + 6

Evaluate

2 (x - 1) (x - 3)

Multiply the terms

More Steps

Evaluate

2 (x - 1)

Apply the distributive property

2 x - 2 \times 1

Any expression multiplied by 1 remains the same

2 x - 2

(2 x - 2) (x - 3)

Apply the distributive property

2 x \times x - 2 x \times 3 - 2 x - (- 2 \times 3)

Multiply the terms

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

Multiply the numbers

2 x^{2} - 6 x - 2 x - (- 2 \times 3)

Multiply the numbers

2 x^{2} - 6 x - 2 x - (- 6)

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

2 x^{2} - 6 x - 2 x + 6

Solution

More Steps

Evaluate

- 6 x - 2 x

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

(- 6 - 2) x

Subtract the numbers

- 8 x

2 x^{2} - 8 x + 6

Show Solution

Find the roots

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

Evaluate

2 (x - 1) (x - 3)

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

2 (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