Solve (a-2)(3a-1)

Question

Simplify the expression

3 a^{2} - 7 a + 2

Evaluate

(a - 2) (3 a - 1)

Apply the distributive property

a \times 3 a - a \times 1 - 2 \times 3 a - (- 2 \times 1)

Multiply the terms

More Steps

Evaluate

a \times 3 a

Use the commutative property to reorder the terms

3 a \times a

Multiply the terms

3 a^{2}

3 a^{2} - a \times 1 - 2 \times 3 a - (- 2 \times 1)

Any expression multiplied by 1 remains the same

3 a^{2} - a - 2 \times 3 a - (- 2 \times 1)

Multiply the numbers

3 a^{2} - a - 6 a - (- 2 \times 1)

Any expression multiplied by 1 remains the same

3 a^{2} - a - 6 a - (- 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

3 a^{2} - a - 6 a + 2

Solution

More Steps

Evaluate

- a - 6 a

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

(- 1 - 6) a

Subtract the numbers

- 7 a

3 a^{2} - 7 a + 2

Show Solution

Find the roots

a_{1} = \frac{1}{3}, a_{2} = 2

Alternative Form

a_{1} = 0. \dot{3}, a_{2} = 2

Evaluate

(a - 2) (3 a - 1)

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

(a - 2) (3 a - 1) = 0

Separate the equation into 2 possible cases

a - 2 = 0 3 a - 1 = 0

Solve the equation

More Steps

Evaluate

a - 2 = 0

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

a = 0 + 2

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

a = 2

a = 2 3 a - 1 = 0

Solve the equation

More Steps

Evaluate

3 a - 1 = 0

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

3 a = 0 + 1

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

3 a = 1

Divide both sides

\frac{3 a}{3} = \frac{1}{3}

Divide the numbers

a = \frac{1}{3}

a = 2 a = \frac{1}{3}

Solution

a_{1} = \frac{1}{3}, a_{2} = 2

Alternative Form

a_{1} = 0. \dot{3}, a_{2} = 2

Show Solution