Solve (4-a)*(2a-1)

Question

Simplify the expression

9 a - 4 - 2 a^{2}

Evaluate

(4 - a) (2 a - 1)

Apply the distributive property

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

Multiply the numbers

8 a - 4 \times 1 - a \times 2 a - (- a \times 1)

Any expression multiplied by 1 remains the same

8 a - 4 - a \times 2 a - (- a \times 1)

Multiply the terms

More Steps

Evaluate

- a \times 2 a

Multiply the numbers

- 2 a \times a

Multiply the terms

- 2 a^{2}

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

Any expression multiplied by 1 remains the same

8 a - 4 - 2 a^{2} - (- a)

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 a - 4 - 2 a^{2} + a

Solution

More Steps

Evaluate

8 a + a

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

(8 + 1) a

Add the numbers

9 a

9 a - 4 - 2 a^{2}

Show Solution

Find the roots

a_{1} = \frac{1}{2}, a_{2} = 4

Alternative Form

a_{1} = 0.5, a_{2} = 4

Evaluate

(4 - a) (2 a - 1)

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

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

Separate the equation into 2 possible cases

4 - a = 0 2 a - 1 = 0

Solve the equation

More Steps

Evaluate

4 - a = 0

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

- a = 0 - 4

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

- a = - 4

Change the signs on both sides of the equation

a = 4

a = 4 2 a - 1 = 0

Solve the equation

More Steps

Evaluate

2 a - 1 = 0

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

2 a = 0 + 1

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

2 a = 1

Divide both sides

\frac{2 a}{2} = \frac{1}{2}

Divide the numbers

a = \frac{1}{2}

a = 4 a = \frac{1}{2}

Solution

a_{1} = \frac{1}{2}, a_{2} = 4

Alternative Form

a_{1} = 0.5, a_{2} = 4

Show Solution