Solve (4v-2)(2v-1)

Question

Simplify the expression

8 v^{2} - 8 v + 2

Evaluate

(4 v - 2) (2 v - 1)

Apply the distributive property

4 v \times 2 v - 4 v \times 1 - 2 \times 2 v - (- 2 \times 1)

Multiply the terms

More Steps

Evaluate

4 v \times 2 v

Multiply the numbers

8 v \times v

Multiply the terms

8 v^{2}

8 v^{2} - 4 v \times 1 - 2 \times 2 v - (- 2 \times 1)

Any expression multiplied by 1 remains the same

8 v^{2} - 4 v - 2 \times 2 v - (- 2 \times 1)

Multiply the numbers

8 v^{2} - 4 v - 4 v - (- 2 \times 1)

Any expression multiplied by 1 remains the same

8 v^{2} - 4 v - 4 v - (- 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

8 v^{2} - 4 v - 4 v + 2

Solution

More Steps

Evaluate

- 4 v - 4 v

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

(- 4 - 4) v

Subtract the numbers

- 8 v

8 v^{2} - 8 v + 2

Show Solution

Factor the expression

2 (2 v - 1)^{2}

Evaluate

(4 v - 2) (2 v - 1)

Evaluate

8 v^{2} - 8 v + 2

Solution

2 (2 v - 1)^{2}

Show Solution

Find the roots

v = \frac{1}{2}

Alternative Form

v = 0.5

Evaluate

(4 v - 2) (2 v - 1)

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

(4 v - 2) (2 v - 1) = 0

Separate the equation into 2 possible cases

4 v - 2 = 0 2 v - 1 = 0

Solve the equation

More Steps

Evaluate

4 v - 2 = 0

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

4 v = 0 + 2

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

4 v = 2

Divide both sides

\frac{4 v}{4} = \frac{2}{4}

Divide the numbers

v = \frac{2}{4}

Cancel out the common factor 2

v = \frac{1}{2}

v = \frac{1}{2} 2 v - 1 = 0

Solve the equation

More Steps

Evaluate

2 v - 1 = 0

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

2 v = 0 + 1

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

2 v = 1

Divide both sides

\frac{2 v}{2} = \frac{1}{2}

Divide the numbers

v = \frac{1}{2}

v = \frac{1}{2} v = \frac{1}{2}

Solution

v = \frac{1}{2}

Alternative Form

v = 0.5

Show Solution